Question

Tangent Be and secant BC intersect at point B. Find the value of x. If necessary, round to the hundredths place.

Answer 1

The value of x is 15.56.

Solution:

Tangent and Secant theorem:

If one secant and one tangent are drawn to a circle from one exterior point, then the square of the length of the tangent is equal to the product of the external secant segment and the total length of the secant.

BE = 22 BD = x, CD = x

BC = x + x = 2x

By the tangent and secant theorem,

$BE^2=BD \cdot BC$

$22^2=x \cdot 2x$

$484= 2x^2$

Divide by 2 on both sides of the equation, we get

$242=x^2$

Take square root on both side of the equation.

x = 15.56

Hence the value of x is 15.56.