Question

OP is equal to 2r ; r is radii<br />P.T - ABP is equilateral

Answer 1

Answer:

Step-by-step explanation:

Join A to B.

We have

OP= Diameter

Or, OQ + OP= diameter

Or, Radius + PQ = diameter (that is OQ=radius)

Or, PQ = diameter – radius

Or, PQ = radius

Or, OQ = PQ = radius

Thus OP is the hypotenuse of the right angle triangle AOP.

So, in ∆AOP sin of angle P = OP /AO

= 1/2

So, P = 30°

Hence, APB = 60°

Now, As in ∆AOP, AP=AB

So, PAB = PBA =60°

Hence,

∆ABP is equilateral triangle.