CBSE Class 10 Answered

Dear Student

From the Image   PA, PB are the two tangents.

Say OP= d   (  d= diameter of rhe circle)

From the right angle triangle PAO     PO cosθ =  AO= r= d/2       ==>   (1)

==>  d cosθ =  d/2   ==>    cosθ=1/2  ==>  θ= 60⁰

AD=DB=  AO sin60 = r  3   / 2  ==>  AB=  3 r                                   ==>  (2)

PA=PB= PO sin 60= d  3  /2   =3  r                                                   ==> (3)

From  equations (2),  (3)     PA=PB=AB= 3  r

Therefore PAB is an equilateral triangle

Regards

Team

Topperlearning