Question

(diagram in comments)
PA, PB, and PC are tangent to the circles as shown in the diagram. Which of the following expresses the length of PA in terms of the lengths of PB and PC?

A) 1/4 (PB + PC)
B) 1/2 (PB + PC)
C) PB + PC
D) 2(PB + PC)
E) It cannot be determined from the information given.

Answer 1

B .
as the tangents are of equal lengths as per theorem which states
if two tangents are drawn on a circle and they cross, the lengths of the two tangents (from the point where they touch the circle to the point where they cross) will be the same.

so PA = PB = PC
ie PA = 1/2 (PB + PC)

Answer 2

refer this http://www.mathsrevision.net/gcse/pages.php?page=13

Answer 3

Thank you for your help!