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Question

ABCD is cyclic quadrilateral. The tangents to a circle at A and C meet at P. If APC = 50, then the value of ADC is:

A
65
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B
70
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C
80
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D
none of these
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Solution

The correct option is A 65
Given APC=500

As the radius is always perpendicular to tangent at the point of contact,
OCP=OAP=900

As AOCP is a quadrilateral, sum of all its interior angles are equal to 3600

AOC=1300[3600(900+900+500)]

We know that, angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc on the circumference of the circle.

ADC=13002
=650

Hence, ADC=650.

915074_376464_ans_e19d4063f91a4dc08fed4b22a49ba280.png

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