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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. - ICSE Class 10 - Mathematics

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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.

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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Solution 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. Concept: Arc and Chord Properties - Angle in a Semi-circle is a Right Angle.
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