Question

please solve this...​

Answer 1

Answer:

Step-by-step explanation:

Say,Radius (OA) = r

OP = 2r………given,OP= diameter of the circle

OAP = 90 (Tangent is  to the radius through the point of contact)

In right OAP

sin (OPA) =

OPA = 30

Similarly OPB = 30

APB = 30 + 30 = 60

Since PA = PB (Lengths of tangents from an external point are equal)

PAB = PBA

In APB,

APB + PAB + PBA = 180 (angle sum property)

60 + 2PAB = 180

PAB = 60

PBA = 60

Since all angles are 60, ABP is equilateral triangle.

Answer 2

Diameter = OP

                = OQ + QP

                = Radius + QP

OQ = PQ = Radius.

Here, OP is the hypotenuse of right angled triangle AOP.

In ΔAOP,

sin∅ = AO/AP

sin∅ = 1/2

∅ = 30°

Thus,

∠APB = 60°

In ΔAOP,

AP = AB

=> ∠PAB = ∠PBA = 60°

Hence, APB is equilateral triangle.

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