Question

What is the value of X when the two secants touch?

Answer 1

Given

Find

the value of x

Step-by-step explanation

as we know when two secants intersect in the exterior circle , then the product of measure of one segment and its external segment is equal to the product of the measure of other secant and its external segment.

so ,

`\begin{gathered} AC* BC=CE* CD \\ (21+x)* x=(14+x+1)(x+1) \\ 21x+x^2=(15+x)(x+1) \\ 21x+x^2=15x+15+x^2+x \\ 5x=15 \\ x=3 \end{gathered}`

Final Answer

Hence , the value of x is 3