page 1 of 30 pages
MATHEMATICS:
Euclidean Geometry
Name: _______________ Surname: __________________
Class: ______
Issued: ________________________
, page 2 of 30 pages
Question 5
In the diagram below, 𝑀 is the centre of the circle 𝐷𝐴𝐵𝐶. 𝐸𝐷𝐹 is a tangent to the circle at
𝐷 and 𝐹𝐵𝐺 is another tangent to the circle at 𝐵.
𝐹
𝐴
140°
12 1
𝐷 2 𝐵
3 3
5 4
28°
1 𝐹
2
𝑀
𝐺
𝐸
𝐶
Calculate the following angles, with reasons:
5.1 𝐶̂ (2)
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̂1
5.2 𝑀 (3)
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5.3 𝐵̂3 (3)
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̂5
5.4 𝐷 (2)
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[10]
, page 3 of 30 pages
Question 6
In the diagram below, 𝑁𝑃 and 𝑁𝑀 are tangents to the circle at 𝑃 and 𝑀. 𝐾 is a point on the
̂ = 𝑥. 𝐿 is a point on 𝐾𝑀 such that
circle 𝐾𝑃, 𝐾𝑀 and 𝑃𝑀 are chords such that 𝐾
𝐾𝑃||𝐿𝑁, 𝐿 and 𝑃 are joined.
𝑁 𝑃
1 1
3
2 2
𝑄
𝑥 𝐾
2 3
1
1 2 𝐿
𝑀
6.1 Prove that 𝑁𝑀𝐿𝑃 is a cyclic quadrilateral. (4)
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6.2 Prove that ∆𝐾𝐿𝑃 is isosceles. (6)
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___________________________________________________________________________
MATHEMATICS:
Euclidean Geometry
Name: _______________ Surname: __________________
Class: ______
Issued: ________________________
, page 2 of 30 pages
Question 5
In the diagram below, 𝑀 is the centre of the circle 𝐷𝐴𝐵𝐶. 𝐸𝐷𝐹 is a tangent to the circle at
𝐷 and 𝐹𝐵𝐺 is another tangent to the circle at 𝐵.
𝐹
𝐴
140°
12 1
𝐷 2 𝐵
3 3
5 4
28°
1 𝐹
2
𝑀
𝐺
𝐸
𝐶
Calculate the following angles, with reasons:
5.1 𝐶̂ (2)
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̂1
5.2 𝑀 (3)
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5.3 𝐵̂3 (3)
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̂5
5.4 𝐷 (2)
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[10]
, page 3 of 30 pages
Question 6
In the diagram below, 𝑁𝑃 and 𝑁𝑀 are tangents to the circle at 𝑃 and 𝑀. 𝐾 is a point on the
̂ = 𝑥. 𝐿 is a point on 𝐾𝑀 such that
circle 𝐾𝑃, 𝐾𝑀 and 𝑃𝑀 are chords such that 𝐾
𝐾𝑃||𝐿𝑁, 𝐿 and 𝑃 are joined.
𝑁 𝑃
1 1
3
2 2
𝑄
𝑥 𝐾
2 3
1
1 2 𝐿
𝑀
6.1 Prove that 𝑁𝑀𝐿𝑃 is a cyclic quadrilateral. (4)
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6.2 Prove that ∆𝐾𝐿𝑃 is isosceles. (6)
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