Question

Need with number 7!

I been struggling with this problem for 20 minutes. It’s been stressing me out. Appreciated if you help me out here.

Answer 1

Answer: 6

SOLUTION

∵segment
`\frac{}{AB}`is tangent to the circle at point C.

∴∠MCA=∠MCB=90°

Suppose
`\frac{}{MC} =x`

From the Pythagorean theorem

MA²=9²+
`x`²

MB²=4²+
`x`²

∴MA²+MB²=AB²

i.e.
`x^(2) +9^(2) +4^(2) +x^(2) =(9+4)^(2) \\2x^(2) +97=169\\2x^(2) =72\\x^(2) =36\\x=6`

We conclude that
`x=6=\frac{}{MC}`