71.ABC is an isosceles triangle with AB = AC. A circle through B and C intersects AD and AC at D and E respectively. Prove that BC || DE.
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72.Prove that the circle drawn on any equal side of an isosceles triangle as diameter, bisects the third side.
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73.
In the figure, D is the centre of a circle. Prove that 2(∠XZY + ∠YXZ) = ∠XPZ]
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Long Answer Type
74.Prove that the opposite angles of an isosceles trapezium are supplementary.
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75.In the figure, O is the centre of the circle. BD = OD and CD ⊥ AB. Find ∠CAB.
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76.If the bisectors of the opposite angles of a cyclic quadrilateral ABCD intersect the circle circumscribing it at the points P and Q, prove that PQ is a diameter of the circle.
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Short Answer Type
77.If O is the centre of a circle as shown in figure, then prove x + y = z.
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78.
5. In the given figure, find the values of a, b, c and d. Given that ∠BCD = 43° and ∠BAE = 62°.
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79.P and Q are centres of the two circles which intersect at B and C. ACD is a straight line. Find the values of x, y, z.
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80.ABCD is a cylic quadrilateral. If AC bisects both the angles A and C then prove that ∠ABC = 90°.
Short Answer Type
Long Answer Type
