Question

In fig., the pair of tangents ap and aq drawn from an external point a to a circle with centre o are perpendicular to each other and length of each tangent is 5 cm. then, find the radius of the circle.

Answer 1

According to Question when we draw figure we get

Tangents AP = AQ

and in triangle APO and Triangle AQO

AP = AQ
AO is Common
OP = OQ
Thus the triangles are similar

Now as we know
that angle in a semicircle is 90 deg
thus

 angle P =angle Q = Angle o =90 deg
thus 
we can say that OP = OQ = AP = AQ
thus the radius of the circle is 5 Cm

Answer 2

Answer:

Step-by-step explanation:

Tangents AP = AQ

In triangle APO and Triangle AQO

AP = AQ

AO =AO (Common)

OP = OQ (radius of same circle)

So, triangle APO and Triangle AQO are similar

Now,POQA is a square

OP = OQ = AP = AQ

We are give AP=AQ= 5 Cm

So, AP=OP (Proved)

Thus, OP= radius= 5Cm