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In the circle $G$, the midpoint of the radius $FG$ is $H$ and $AB\perp  EF$ at $H$. The semicircle with $AB $ as diameter intersects $EF $ in $I$, line $AI $ intersects circle $G$ in $C$ and line $BI$ intersects the circle $G$ at $D$, then chord $BC$ is drawn.

If the radius of the circle $G$ is $r$, then find length of chord $BC$ in terms of $r$.

 

 Feb 5, 2021
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Triangle BCG is an isosceles right triangle.

 

BG and CG are the radii of a circle G.

 

(BC)2 = 2r           BC = r√2

 Feb 10, 2021

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