Mathematics
In the figure (i) given below, O is the center of the circle. If ∠BAD = 30°, find the values of p, q and r.
Circles
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Answer
From figure,
ABCD is a cyclic quadrilateral as all vertices lie on the circumference of the circle.
Sum of opposite angles of cyclic quadrilateral = 180°
⇒ ∠A + ∠C = 180°
⇒ 30° + p = 180°
⇒ p = 180° - 30°
⇒ p = 150°.
∠BAD = ∠BED (∵ angles in same segment are equal.)
⇒ r = 30°.
Arc BD subtends ∠BAD at point A and ∠BOD at center.
∠BOD = 2∠BAD (∵ angle subtended by an arc at center is double the angle subtended at any other point of the circle.)
q = 2 × 30°
q = 60°.
Hence, the value of p = 150°, q = 60° and r = 30°.
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