Need with number 7!

Mathematics

1 answer:

topjm [15]3 years ago

7 0

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

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