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?

Answer 1

x=3

Explanation:

This is brilliant!!!!!!!!

Answer 2

x=3

Explanation:

The diagram is attached.

To solve this we apply the theorem of intersecting secants.

By this theorem, in the diagram:

`DC X EC =BC X AC`

(x+1) X (14+x+1) = x X (21+x)

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

Expand the brackets

`(x+1)(15+x)=x(21+x)\\15x+x^2+15+x=21x+x^2\\\text{Collect like terms and simplify}\\15x+x^2+15+x-21x-x^2=0\\15x+x-21x+15=0\\-5x=-15\\$Divide both sides by -5\\x=3`