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91. ABCD is a cyclic quadrilateral. O is the centre of the circle. If ∠BOD = 160°, find ∠BPD.

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92. In the figure, ∠AOB = 90° and ∠ABC = 30°, then find the measure of ∠CAO.

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93. In figure, O is the centre of the circle. If ∠AOB = 80°, then find the measures of ∠ADB and ∠ACB.

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94. In adjacent figure, two chords AB and CD of a circle intersect at right angle. If ∠ABD = 65°, find the measure of ∠CAB.

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95.

In figure ABCD is a cyclic quadrilateral in which AB is extended till F and BE || DC. If ∠FBE = 20° and ∠DAB = 95°, then find ∠ADC.

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96. In adjoining figure, ∠ABC = 95°, ∠ACB = 35°, find ∠BDC.

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97. If diagonals of a cyclic quadrilateral are diameters of the circle and perpendicular to each other, prove that it is a square.

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98. PQRS in a cyclic quadrilateral, in which ∠P = 2x°, ∠Q = y°, ∠R = 3x° and ∠S = 2y°. Find the values of x and y.

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99.

In the figure, ABCD is a cyclic quadrilateral in which AC and BD and its diagonals. If ∠DBC = 55° and ∠BAC = 45°, find ∠BCD.

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100. AOB is a diameter of a circle with centre O and C is a point on the circle. Check whether AC² + BC² = AB². Give reasons.

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