Paper 22 Q13IGCSE 0580 May/June 2023

Question

13 D NOT TO SCALE E 32° A C x° B A, B, C and D are points on a circle. AB is parallel to DC and angle ACD=32°. Chords AC and DB intersect at E. Find the value of x

Diagram: # Diagram Description **Diagram type:** Circle with inscribed quadrilateral and intersecting chords **Key measurements/labels:** - Points A, B, C, D on a circle - Angle ACD = 32° - Angle at B = x° - Point E where chords AC and DB intersect - AB is parallel to DC (indicated by parallel line markers) **Key relationships:** - "NOT TO SCALE" notice present - AB || DC (parallel lines marked) - Chords AC and DB intersect at point E inside the circle - Cyclic quadrilateral ABCD inscribed in the circle

This question tests your understanding of cyclic quadrilaterals and parallel chord properties in circle geometry. You need to use the fact that opposite angles in a cyclic quadrilateral sum to 180° and apply properties of parallel lines.

Step-by-Step Solution

Key Takeaway

In cyclic quadrilaterals with parallel chords, combine alternate angle properties with the fact that opposite angles sum to 180°.

Common Mistakes

Confusing alternate angles with corresponding angles when dealing with parallel lines AB and DC
Forgetting that opposite angles in a cyclic quadrilateral sum to 180°, not that all angles sum to 360°

Exam Tip

When you see parallel chords in a circle, look for alternate angles first, then apply cyclic quadrilateral properties to find the unknown angle.

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