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Question
In the figure, given alongside, AB || CD and O is the centre of the circle. If ∠ADC = 25°; find the angle AEB. Give reasons in support of your answer.
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Solution
Join AC and BD
∴ ∠CAD = 90° and ∠CBD = 90°
(Angle in a semicircle is a right angle)
Also, AB || CD
∴ ∠BAD = ∠ADC = 25° ...(Alternate angles)
∠BAC = ∠BAD + ∠CAD
= 25° + 90°
= 115°
∴ ∠ADB = 180° – 25° – ∠BAC
= 180° – 25° – 115°
= 40°
(Pair of opposite angles in a cyclic quadrilateral are supplementary)
Also, ∠AEB = ∠ADB = 40°
(Angle subtended by the same chord on the circle are equal)
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