Opposite angles of a cyclic quadrilateral are supplementary. (2x + 10) + (3x – 20) = 180 5x – 10 = 180 x = 38 Thus, ∠P = 86° and ∠R = 94°.
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In a cyclic quadrilateral, opposite angles are supplementary. Therefore, ∠C = 180° – 75° = 105°. Similarly, ∠D = 180° – 110° = 70°.
Since AB is the diameter of the circle, the angle subtended by the diameter at any point on the circumference is 90°. Therefore, ∠ACB = 90°.
Let AB be a chord and O be the centre. Since OA = OB, O is equidistant from A and B. Therefore, O lies on the perpendicular bisector of AB. Hence proved.
The perpendicular from the centre to the chord bisects the chord. With radius 15 cm and distance 9 cm, half the chord is 12 cm. Therefore, the chord length is 24 cm.