Geometry problem 7 by Dhaval Furia

Geometry Level pending

$AB$ is a diameter of a circle of radius $5$ . Let $P$ and $Q$ be two points on the circle so that the length of $PB$ is $6$ , and the length of $AP$ is twice that of $AQ$ . What value is the length of $QB$ is nearest to?

8.5

9.1

7.8

9.3

1 solution

A Former Brilliant Member
Jun 14, 2020

Let $|\overline {AQ}|=x, |\overline {AP}|=2x,|\overline {QB}|=y$ .

Then $x^2+y^2=10^2=100,4x^2+36=100\implies x=4\implies y=\sqrt {84}\approx \boxed {9.165}$ .

Geometry problem 7 by Dhaval Furia

1 solution

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