Question 14 — IGCSE 0580 Oct/Nov 2025 Paper 21
Cambridge IGCSE Mathematics 0580, Extended tier, non-calculator. Topic: Geometry · Angles using geometrical properties. Worth 9 marks.
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Question text
14
C
55°
NOT TO
B SCALE
X
88°
A
D
E
A, B, C, D and E lie on the circle.
AC and BD intersect at X.
Angle ACD = 55° and angle CXD = 88°.
(a) Complete the statements, giving a geometrical reason in each part.
Angle CDB = ......................... because ......................................................................................
.....................................................................................................................................................
Angle ABD = ......................... because ......................................................................................
.....................................................................................................................................................
Angle AED = ......................... because ......................................................................................
.....................................................................................................................................................
[6]
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© UCLES 2025 (cid:300)(cid:263)(cid:180)(cid:250)(cid:219)(cid:299)(cid:248)(cid:289)(cid:205)(cid:237)(cid:256)(cid:256)(cid:276)(cid:234)(cid:245)(cid:233)(cid:258)(cid:258) 0580/21/O/N/25
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* 0000800000009 *
9
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(b) Triangle CXD is mathematically similar to triangle BXA.
DX = 8.0 cm, BX = 2.7 cm and AX = 4.0 cm.
(i) Work out the length of CX.
CX = ........................................... cm [2]
(ii) Complete the statement.
Area of triangle CXD : area of triangle BXA = ....................... : ....................... [1]
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DFD
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