A, B, C, D and E lie on the circle. AC and BD intersect at X. Angle ACD = 55° and angle CXD = 88°.

Описание: 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 ........................ [6m]

(b) Triangle CXD is mathematically similar to triangle BXA.
DX = 8.0cm, BX = 2.7cm and AX = 4.0cm.
(i) Work out the length of CX.
CX = ............................ cm [2m]

(ii) Complete the statement.
Area of triangle CXD : area of triangle BXA = ..................: ................. [1m]

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We’ll break down:
✅ How to find the missing angles using angle sum property of triangle and circle theorems.
✅ How to find the length of the side of a triangle using properties of similar shapes
✅ How to find the ratio of areas of triangles using properties of similar shapes

This question tests your skills in understanding, analyzing and applying the appropriate circle theorems and properties of similar shapes to solve the questions— a must-know Mensuration topic for IGCSE Maths success.

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The question is referred from CIE IGCSE 0580 Mathematics Non-Calculator Extended Paper 21 October November 2025, (0580/21/O/N/25), 0580 w25 qp 21 for educational purpose only.

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📌 Perfect for students revising IGCSE 0580 Extended or Core paper and anyone aiming to boost exam confidence.

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