Question

Need with number 7!

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 $x=6=\frac{}{MC}$