Question

A circle is shown. Secants E C and A C intersect at point C outside of the circle. Secant E C intersects the circle at point D. Secant A C intersects the circle at point B. The length of E D is 14, the length of D C is x + 1, the length of A B is 21, and the length of B C is x. What is the value of x? x = 2 x = 3 x = 4 x = 6

Answer 1

B. x=3

Explanation:

Answer 2

x = 3

Explanation:

Data

• DE = 14 units

• CD = x + 1 units

• BA = 21 units

• CB = x units

Therefore:

• CE = CD + DE = x + 1 + 14 = x + 15 units

• CA = CB + BA = x + 21 units

From Intersecting Secants Theorem :

CD*CE = CB*CA

Replacing with data:

(x + 1)*(x + 15) = x*(x + 21)

x² + 15x + x + 15 = x² + 21x

x² + 15x + x + 15 -x² - 21x = 0

15 - 5x = 0

15 = 5x

15/5 = x

3 = x