Geometry homework

Question

Help !

SP and SR are tangent to circle Q. If SP = 10x - 18 and SR = 2x + 6, find x.

A. 3

B. 2

C. -3

D. -1

Answer 1

The Two-Tangent Theorem states that if two tangent segments are drawn to one circle from the same external point, then they are congruent.

SP=SR

Therefore

10x - 18 = 2x + 6

Subtract 2x from both sides

8x-18=6

Add 18 to both sides

8x=24

Divide both sides by 8

x=3

Answer is A