Question

Find the measure of line segment MK. K 8 I 7 J M 5 2x+1​

Answer 1

Hello!

This is a problem about relating circle theorems to line lengths.

We can first see that both line segment MK and CM are secants within the circle that come from a common point K.

This means that the Intersecting Secant Theorem applies here.

The Intersecting Secant Theorem states that if two secants are formed from a common point outside the circle, the length of each secant multiplied by the length of its corresponding external secant are equivalent.

We can set up the following equation.

$8(8+x+5)=7(7+2x+1)$

$8(x+13)=7(2x+8)$

$8x+104=14x+56$

$6x=48$

$x=8$

Using this value, we can find the length of line segment MK.

$MK=x+5+8$

$MK=8+5+8$

$MK=21$

Hope this helps!