Question

to draw a pair of tangents to a circle which are inclined at each other at an angle 30 degree it is required to draw two tangents at end pints of those two radii of the circke ,the angle between them should be ​

Answer 1

Answer:

Suppose that O be the center of the circle and  P and Q be any 2 points on the circle.

Draw tangents through P and Q such that two tangents meet at A outside the circle and angle PAQ=65

We know all tangents are perpendicular to radii at the points of contact

So OPAQ is a cyclic quadrilateral . The angles PAQ and POQ are supplementary.

Therefore angle POQ=180–65=115

Answer 2

ATQ,B=30°

BY SUM ANGLE PROPERTY OF A QUADRILAATERAL

A+B+C+O=360°⇒(1)

A=B=90°(TANGENT⊥ RADIOUS)⇒(2)

∴90°+30°+90°+O=360°

O=360°-210°

O=150°

HENCE THE ANGLE BTW THEM MUST BE 150°