NCSSM PLACEMENT EXAM Q&A 2026 STUDY
GUIDE QUESTIONS WITH ANSWERS GRADED
A+
◉ Intersection of a tangent and a radius . Answer: form right angles
when they intersect.
◉ Equation of a circle . Answer: x minus h squared plus y minus k
squared equals radius squared.
◉ Circumference of a circle . Answer: 2 times pi times radius or pi
times diameter.
◉ Area of a circle . Answer: pi times radius squared.
◉ Central angle . Answer: is equal to its intercepted arc.
◉ Inscribed angle . Answer: is equal to ½ its intercepted arc.
◉ Angle formed by 2 chords intersecting in a circle . Answer: is equal
to the sum of the arcs divided by 2.
,◉ Angle formed by 2 secants . Answer: is equal to the major arc minus
the minor arc divided by 2.
◉ Angle formed by a secant and a tangent . Answer: is equal to the
major arc minus the minor arc divided by 2.
◉ Angle formed by two tangents . Answer: is equal to the major arc
minus the minor arc divided by 2.
◉ Lengths of 2 intersecting chords . Answer: part of the first chord
times the other part of the first chord equals a part of the second chord
times the other part of the second chord.
◉ Lengths of an intersecting diameter and chord that meet at right
angles (perpendicular) . Answer: if a diameter meets a chord at a right
angle (perpendicular), the diameter divides the chord into 2 equal parts.
◉ Lengths of 2 intersecting secants . Answer: the whole length of the
first secant times the outside length of the first secant equals the whole
length of the second secant times the outside length of the second secant.
◉ Lengths of an instersecting secant and tangent . Answer: the whole
length of the first secant times the outside length of the first secant
equals the length of the tangent squared.
,◉ Lengths of intersecting tangents . Answer: Tangents to a circle
sharing a common vertex are equal.
◉ Angles . Answer: acute angles are less than 90 degrees. Right angles
are 90 degrees. obtuse angles are between 90 and 180 degrees. Straight
angles are 180 degrees and reflex angles are greater than 180 degrees.
◉ Adjacent angles . Answer: share a common vertex, a common side,
but not common interior points.
◉ Complementary angles . Answer: 2 angles when added together that
equal 90 degrees.
They do not have to be adjacent angles.
◉ Supplementary angles . Answer: 2 angles when added together that
equal 180 degrees.They do not have to be adjacent angles.
◉ Vertical angles . Answer: vertical angles are congruent.
◉ Alternate interior angles . Answer: alternate interior angles are
congruent.
◉ Corresponding angles . Answer: corresponding angles are congruent.
, ◉ Sum of the angles in a triangle . Answer: the 3 angles of a triangle
add up to 180 degrees.
◉ Triangles classified by sides . Answer: scalene triangles have no
equal sides.
isosceles triangles have at least 2 equal sides.
equilateral triangles have 3 equal sides.
◉ Triangles classified by angles . Answer: acute triangles have 3 acute
angles.
right triangles have a 90 degree and 2 acute angles.
obtuse triangles have an obtuse and 2 acute angles.
◉ Exterior angle of a triangle . Answer: the exterior angle of a triangle
equals the sum of the 2 opposite interior angles.
◉ Isosceles triangles . Answer: sides opposite congruent angles are
congruent.
angles opposite congruent sides are congruent.
◉ Triangle inequality theorem . Answer: the sum of 2 sides of a
triangle must be greater than the 3rd side.
GUIDE QUESTIONS WITH ANSWERS GRADED
A+
◉ Intersection of a tangent and a radius . Answer: form right angles
when they intersect.
◉ Equation of a circle . Answer: x minus h squared plus y minus k
squared equals radius squared.
◉ Circumference of a circle . Answer: 2 times pi times radius or pi
times diameter.
◉ Area of a circle . Answer: pi times radius squared.
◉ Central angle . Answer: is equal to its intercepted arc.
◉ Inscribed angle . Answer: is equal to ½ its intercepted arc.
◉ Angle formed by 2 chords intersecting in a circle . Answer: is equal
to the sum of the arcs divided by 2.
,◉ Angle formed by 2 secants . Answer: is equal to the major arc minus
the minor arc divided by 2.
◉ Angle formed by a secant and a tangent . Answer: is equal to the
major arc minus the minor arc divided by 2.
◉ Angle formed by two tangents . Answer: is equal to the major arc
minus the minor arc divided by 2.
◉ Lengths of 2 intersecting chords . Answer: part of the first chord
times the other part of the first chord equals a part of the second chord
times the other part of the second chord.
◉ Lengths of an intersecting diameter and chord that meet at right
angles (perpendicular) . Answer: if a diameter meets a chord at a right
angle (perpendicular), the diameter divides the chord into 2 equal parts.
◉ Lengths of 2 intersecting secants . Answer: the whole length of the
first secant times the outside length of the first secant equals the whole
length of the second secant times the outside length of the second secant.
◉ Lengths of an instersecting secant and tangent . Answer: the whole
length of the first secant times the outside length of the first secant
equals the length of the tangent squared.
,◉ Lengths of intersecting tangents . Answer: Tangents to a circle
sharing a common vertex are equal.
◉ Angles . Answer: acute angles are less than 90 degrees. Right angles
are 90 degrees. obtuse angles are between 90 and 180 degrees. Straight
angles are 180 degrees and reflex angles are greater than 180 degrees.
◉ Adjacent angles . Answer: share a common vertex, a common side,
but not common interior points.
◉ Complementary angles . Answer: 2 angles when added together that
equal 90 degrees.
They do not have to be adjacent angles.
◉ Supplementary angles . Answer: 2 angles when added together that
equal 180 degrees.They do not have to be adjacent angles.
◉ Vertical angles . Answer: vertical angles are congruent.
◉ Alternate interior angles . Answer: alternate interior angles are
congruent.
◉ Corresponding angles . Answer: corresponding angles are congruent.
, ◉ Sum of the angles in a triangle . Answer: the 3 angles of a triangle
add up to 180 degrees.
◉ Triangles classified by sides . Answer: scalene triangles have no
equal sides.
isosceles triangles have at least 2 equal sides.
equilateral triangles have 3 equal sides.
◉ Triangles classified by angles . Answer: acute triangles have 3 acute
angles.
right triangles have a 90 degree and 2 acute angles.
obtuse triangles have an obtuse and 2 acute angles.
◉ Exterior angle of a triangle . Answer: the exterior angle of a triangle
equals the sum of the 2 opposite interior angles.
◉ Isosceles triangles . Answer: sides opposite congruent angles are
congruent.
angles opposite congruent sides are congruent.
◉ Triangle inequality theorem . Answer: the sum of 2 sides of a
triangle must be greater than the 3rd side.
