Given:RS = 6 RV = 14. Find:RT Let RT = x. Use the theorem to write an equation relating the values of RS, RT, and RV in terms of x. Find RT.

Question

Consider the following theorem.

If a tangent segment and a secant segment are drawn to a circle from an external point, then the square of the length of the tangent equals the product of the length of the secant with the length of its external segment.

RS

 is tangent to the circle at S.

1. 
   

Given:RS = 6

RV = 14

Find:RT

Let RT = x.

Use the theorem to write an equation relating the values of RS, RT, and RV in terms of x.

 

Find RT.

RT = 

 

Answer 1

WE know Theorem: RS² = RV·RT; from xere x = RT = RS²/RV = 6²/14 = 18/7

Answer 2

If a tangent segment and a secant segment are drawn to a circle from an external point, then the square of the length of the tangent equals the product of the length of the secant with the length of its external segment.

The square of the length of the tangent is RS² = 6² = 36.

Equals the product of the length of the secant (RV = 14) and its external segment (RT):

RS² = RV·RT

6² = 14·RT or, in terms of x, 6² = 14x

Solve for x (RT).