Question

a pair of perpendicular tangent are drawn to a circle from an external point.prove that the length of the tangent is equal to the radius of the circle.if the circle is 5 cm ,then find the length of the line joining centre of the circle to the external point.​

Answer 1

Answer:

Step-by-step explanation:

It is given that a pair of perpendicular tangents are drawn to the circle that means ∠APB=90  

0

 as shown in the above figure:

Therefore,  

PA=PB     (Tangents from the external point P)

∠PAO=∠PBO=90  

0

     (Radius and tangents are perpendicular)

OA=OB     (Radii of same circle)

Thus, AOBP is a square.

Now we have AP=PB=OA=OB

Hence, the length of tangent is equal to radii of the circle.