Question

QUESTION--: What should be the angle between the two tangents which is drawn at the end of two radii and are inclined at an angle of 45 degrees?Yar koi to explain kardo please.​

Answer 1

Answer:

Suppose O be the centre of the circle and PA and PB be the two tangents drawn from P to the circle so that angle APB= 60°

Join OP,OA and OB.

Then angle OAP= angle OBP = 90° and

angle OPA = angle OPB = 30°

OA = OB = 3 cm.

In the right triangle OAP,

OA/AP = tan 30° => 3/AP = 1/√3

So AP= 3√3cm or3×1.732=5.196 cm

So length of each tangent = 5.196 cm.

Answer 2

Answer:

Given- O is the centre of a circle to which a pair of tangents PQ&PR from a point Ptouch the circle at Q&R  respectively. ∠RPQ=60o. 

To find out- ∠ROQ=? 

Solution- ∠OQP=90o=∠ORP since the angle, between a tangent to  a circle and the radius of the same circle passing through  the point of contact, is 90o. ∴  By angle sum property of quadrilaterals, we get ∠OQP+∠RPQ+∠ORP+∠ROQ=360o⟹90o+60o+90o+∠ROQ=360o⟹∠ROQ=120o.