NCSSM PLACEMENT TEST QUESTIONS AND
ANSWERS LATEST UPDATE (2025)!!
Tangent g- ganswersintersects ga gcircle gin gonly g1 gplace.
Secant g- ganswersintersects ga gcircle gin g2 gplaces.
Intersection gof ga gtangent gand ga gradius g- ganswersform gright gangles gwhen gthey gintersect.
Equation gof ga gcircle g- ganswersx gminus gh gsquared gplus gy gminus gk gsquared gequals gradius
gsquared.
Circumference gof ga gcircle g- ganswers2 gtimes gpi gtimes gradius gor gpi gtimes gdiameter.
Area gof ga gcircle g- ganswerspi gtimes gradius gsquared.
Central gangle g- ganswersis gequal gto gits gintercepted garc.
Inscribed gangle g- ganswersis gequal gto g½ gits gintercepted garc.
Angle gformed gby g2 gchords gintersecting gin ga gcircle g- ganswersis gequal gto gthe gsum gof gthe
garcs gdivided gby g2.
Angle gformed gby g2 gsecants g- ganswersis gequal gto gthe gmajor garc gminus gthe gminor garc
gdivided gby g2.
,Angle gformed gby ga gsecant gand ga gtangent g- ganswersis gequal gto gthe gmajor garc gminus gthe
gminor garc gdivided gby g2.
Angle gformed gby gtwo gtangents g- ganswersis gequal gto gthe gmajor garc gminus gthe gminor garc
gdivided gby g2.
Lengths gof g2 gintersecting gchords g- ganswerspart gof gthe gfirst gchord gtimes gthe gother gpart gof
gthe gfirst gchord gequals ga gpart gof gthe gsecond gchord gtimes gthe gother gpart gof gthe gsecond
gchord.
Lengths gof gan gintersecting gdiameter gand gchord gthat gmeet gat gright gangles g(perpendicular)
g- ganswersif ga gdiameter gmeets ga gchord gat ga gright gangle g(perpendicular), gthe gdiameter
gdivides gthe gchord ginto g2 gequal gparts.
Lengths gof g2 gintersecting gsecants g- ganswersthe gwhole glength gof gthe gfirst gsecant gtimes gthe
goutside glength gof gthe gfirst gsecant gequals gthe gwhole glength gof gthe gsecond gsecant gtimes
gthe goutside glength gof gthe gsecond gsecant.
Lengths gof gan ginstersecting gsecant gand gtangent g- ganswersthe gwhole glength gof gthe gfirst
gsecant gtimes gthe goutside glength gof gthe gfirst gsecant gequals gthe glength gof gthe gtangent
gsquared.
Lengths gof gintersecting gtangents g- ganswersTangents gto ga gcircle gsharing ga gcommon gvertex
gare gequal.
Angles g- ganswersacute gangles gare gless gthan g90 gdegrees. gRight gangles gare g90 gdegrees.
gobtuse gangles gare gbetween g90 gand g180 gdegrees. gStraight gangles gare g180 gdegrees gand
greflex gangles gare ggreater gthan g180 gdegrees.
,Adjacent gangles g- ganswersshare ga gcommon gvertex, ga gcommon gside, gbut gnot gcommon
ginterior gpoints.
Complementary gangles g- ganswers2 gangles gwhen gadded gtogether gthat gequal g90 gdegrees.
They gdo gnot ghave gto gbe gadjacent gangles.
Supplementary gangles g- ganswers2 gangles gwhen gadded gtogether gthat gequal g180
gdegrees.They gdo gnot ghave gto gbe gadjacent gangles.
Vertical gangles g- ganswersvertical gangles gare gcongruent.
Alternate ginterior gangles g- ganswersalternate ginterior gangles gare gcongruent.
Corresponding gangles g- ganswerscorresponding gangles gare gcongruent.
Sum gof gthe gangles gin ga gtriangle g- ganswersthe g3 gangles gof ga gtriangle gadd gup gto g180
gdegrees.
Triangles gclassified gby gsides g- ganswersscalene gtriangles ghave gno gequal gsides.
isosceles gtriangles ghave gat gleast g2 gequal gsides.
equilateral gtriangles ghave g3 gequal gsides.
Triangles gclassified gby gangles g- ganswersacute gtriangles ghave g3 gacute gangles.
right gtriangles ghave ga g90 gdegree gand g2 gacute gangles.
obtuse gtriangles ghave gan gobtuse gand g2 gacute gangles.
, Exterior gangle gof ga gtriangle g- ganswersthe gexterior gangle gof ga gtriangle gequals gthe gsum gof
gthe g2 gopposite ginterior gangles.
Isosceles gtriangles g- ganswerssides gopposite gcongruent gangles gare gcongruent.
angles gopposite gcongruent gsides gare gcongruent.
Triangle ginequality gtheorem g- ganswersthe gsum gof g2 gsides gof ga gtriangle gmust gbe ggreater
gthan gthe g3rd gside.
Mid gsegment gof ga gtriangle g- ganswersa gmid gsegment gconnects gthe gmidpoint gof g2 gsides gof
ga gtriangle gand gis gequal gto g½ gthe gside gnot gcontaining gthe g2 gmidpoints.
Median g- ganswersbisects gthe gopposite gside ginto g2 gcongruent gline gsegments.
they gmeet gin ga gtriangle gat ga gpoint gcalled gthe gcentroid.
median gsegments gare gin ga gratio gof g2 gto g1.
Angle gbisector g- ganswersbisects gan gangle ginto g2 gcongruent gangles.
they gmeet gin ga gtriangle gat ga gpoint gcalled gthe gincenter.
Altitude g- ganswersmakes ga gright gangle gwith gthe gopposite gside.
they gmeet gin ga gtriangle gat ga gpoint gcalled gthe gorthocenter.
Perpendicular gbisector g- ganswersbisects gand gmakes ga gright gangle gwith ga gside gof ga
gtriangle.They gmeet gin ga gtriangle gat ga gpoint gcalled gthe gcircumcenter.
Similar gtriangles g- ganswersangles gin gsimilar g(∼) gtriangles gare gcongruent.
sides gare gin gproportion.
ANSWERS LATEST UPDATE (2025)!!
Tangent g- ganswersintersects ga gcircle gin gonly g1 gplace.
Secant g- ganswersintersects ga gcircle gin g2 gplaces.
Intersection gof ga gtangent gand ga gradius g- ganswersform gright gangles gwhen gthey gintersect.
Equation gof ga gcircle g- ganswersx gminus gh gsquared gplus gy gminus gk gsquared gequals gradius
gsquared.
Circumference gof ga gcircle g- ganswers2 gtimes gpi gtimes gradius gor gpi gtimes gdiameter.
Area gof ga gcircle g- ganswerspi gtimes gradius gsquared.
Central gangle g- ganswersis gequal gto gits gintercepted garc.
Inscribed gangle g- ganswersis gequal gto g½ gits gintercepted garc.
Angle gformed gby g2 gchords gintersecting gin ga gcircle g- ganswersis gequal gto gthe gsum gof gthe
garcs gdivided gby g2.
Angle gformed gby g2 gsecants g- ganswersis gequal gto gthe gmajor garc gminus gthe gminor garc
gdivided gby g2.
,Angle gformed gby ga gsecant gand ga gtangent g- ganswersis gequal gto gthe gmajor garc gminus gthe
gminor garc gdivided gby g2.
Angle gformed gby gtwo gtangents g- ganswersis gequal gto gthe gmajor garc gminus gthe gminor garc
gdivided gby g2.
Lengths gof g2 gintersecting gchords g- ganswerspart gof gthe gfirst gchord gtimes gthe gother gpart gof
gthe gfirst gchord gequals ga gpart gof gthe gsecond gchord gtimes gthe gother gpart gof gthe gsecond
gchord.
Lengths gof gan gintersecting gdiameter gand gchord gthat gmeet gat gright gangles g(perpendicular)
g- ganswersif ga gdiameter gmeets ga gchord gat ga gright gangle g(perpendicular), gthe gdiameter
gdivides gthe gchord ginto g2 gequal gparts.
Lengths gof g2 gintersecting gsecants g- ganswersthe gwhole glength gof gthe gfirst gsecant gtimes gthe
goutside glength gof gthe gfirst gsecant gequals gthe gwhole glength gof gthe gsecond gsecant gtimes
gthe goutside glength gof gthe gsecond gsecant.
Lengths gof gan ginstersecting gsecant gand gtangent g- ganswersthe gwhole glength gof gthe gfirst
gsecant gtimes gthe goutside glength gof gthe gfirst gsecant gequals gthe glength gof gthe gtangent
gsquared.
Lengths gof gintersecting gtangents g- ganswersTangents gto ga gcircle gsharing ga gcommon gvertex
gare gequal.
Angles g- ganswersacute gangles gare gless gthan g90 gdegrees. gRight gangles gare g90 gdegrees.
gobtuse gangles gare gbetween g90 gand g180 gdegrees. gStraight gangles gare g180 gdegrees gand
greflex gangles gare ggreater gthan g180 gdegrees.
,Adjacent gangles g- ganswersshare ga gcommon gvertex, ga gcommon gside, gbut gnot gcommon
ginterior gpoints.
Complementary gangles g- ganswers2 gangles gwhen gadded gtogether gthat gequal g90 gdegrees.
They gdo gnot ghave gto gbe gadjacent gangles.
Supplementary gangles g- ganswers2 gangles gwhen gadded gtogether gthat gequal g180
gdegrees.They gdo gnot ghave gto gbe gadjacent gangles.
Vertical gangles g- ganswersvertical gangles gare gcongruent.
Alternate ginterior gangles g- ganswersalternate ginterior gangles gare gcongruent.
Corresponding gangles g- ganswerscorresponding gangles gare gcongruent.
Sum gof gthe gangles gin ga gtriangle g- ganswersthe g3 gangles gof ga gtriangle gadd gup gto g180
gdegrees.
Triangles gclassified gby gsides g- ganswersscalene gtriangles ghave gno gequal gsides.
isosceles gtriangles ghave gat gleast g2 gequal gsides.
equilateral gtriangles ghave g3 gequal gsides.
Triangles gclassified gby gangles g- ganswersacute gtriangles ghave g3 gacute gangles.
right gtriangles ghave ga g90 gdegree gand g2 gacute gangles.
obtuse gtriangles ghave gan gobtuse gand g2 gacute gangles.
, Exterior gangle gof ga gtriangle g- ganswersthe gexterior gangle gof ga gtriangle gequals gthe gsum gof
gthe g2 gopposite ginterior gangles.
Isosceles gtriangles g- ganswerssides gopposite gcongruent gangles gare gcongruent.
angles gopposite gcongruent gsides gare gcongruent.
Triangle ginequality gtheorem g- ganswersthe gsum gof g2 gsides gof ga gtriangle gmust gbe ggreater
gthan gthe g3rd gside.
Mid gsegment gof ga gtriangle g- ganswersa gmid gsegment gconnects gthe gmidpoint gof g2 gsides gof
ga gtriangle gand gis gequal gto g½ gthe gside gnot gcontaining gthe g2 gmidpoints.
Median g- ganswersbisects gthe gopposite gside ginto g2 gcongruent gline gsegments.
they gmeet gin ga gtriangle gat ga gpoint gcalled gthe gcentroid.
median gsegments gare gin ga gratio gof g2 gto g1.
Angle gbisector g- ganswersbisects gan gangle ginto g2 gcongruent gangles.
they gmeet gin ga gtriangle gat ga gpoint gcalled gthe gincenter.
Altitude g- ganswersmakes ga gright gangle gwith gthe gopposite gside.
they gmeet gin ga gtriangle gat ga gpoint gcalled gthe gorthocenter.
Perpendicular gbisector g- ganswersbisects gand gmakes ga gright gangle gwith ga gside gof ga
gtriangle.They gmeet gin ga gtriangle gat ga gpoint gcalled gthe gcircumcenter.
Similar gtriangles g- ganswersangles gin gsimilar g(∼) gtriangles gare gcongruent.
sides gare gin gproportion.
