Question

Two tangents are drawn to a circle from an external point P. touching the circle at the points A and B. A third tangent intersects segment PA in C and segment PB in D and touches the circle at Q. if PA = 20 units, find the perimeter of Δ  PCD. 

Answer 1

PA = PB = 20 Units ---(1) {Length of tangents drawn from an external point to a circle are equal }

CQ = CA and DQ = DB

Perimeter of Δ PCD 

= PC+ CD+ PD

= PC+ CQ + QD + PD      {Using {1)} 

= PA+ PB 

= 2PA 

= 2{20}  

= 40 Units