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Question

To draw a pair of tangents to a circle which are inclined to each other at an angle of 35, it is required to draw tangents at the end point of those two radii of the circle, the angle between them is:

A
70
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B
110
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C
140
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D
145
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Solution

The correct option is D 145



PA and PB are tangents drawn from an external point P to the circle.

OAP=OBP=90 (Radius is perpendicular to the tangent at point of contact)

In quadrilateral OAPB,

APB+OAB+AOB+OBP=360

35+90+AOB+90=360

215 +AOB = 360

AOB=360280=145

Thus, the angle between the two radii, OA and OB is 145.


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