QQuestion
In the given figure, ABCD is a cyclic quadrilateral. DE is produced to E and ∠CDE = 65°. If x is the angle subtended by chord AC at the centre, then x is:
(a) 32.5°
(b) 65°
(c) 115°
(d) 130°
ICSEClass XMathematicsCircles01 Mark2026 Moderate
✓Answer
(d) 130°
Explanation:
The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.
Therefore, ∠ABC = ∠CDE = 65°.
The angle subtended by an arc at the centre is twice the angle subtended by the same arc at any point on the remaining part of the circle.
∠AOC = 2 × ∠ABC
x = 2 × ∠ABC
⇒ x = 2 × 65° = 130°.
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