Circle Geo Question (1 Viewer)

pikachu975 · Jan 16, 2017

http://prntscr.com/dw7c2q

Hi, just need help with part b. Answer is 28.125 cm. Thanks!

InteGrand · Jan 16, 2017

pikachu975 said:
http://prntscr.com/dw7c2q

Hi, just need help with part b. Answer is 28.125 cm. Thanks!

$\noindent Let $r$ be the radius of the circle $\mathcal{C}$ with diameter $CF$. Once we find this, we are pretty much done (answer will be $CE = 2r-2 = 2(r-1)$). Consider $\triangle OAE$, where $O$ is the centre of $\mathcal{C}$. Then Pythagoras' Theorem here gives $r^{2} = (r-2)^{2} + (7.5)^{2}$, as $OA = r$, $OE = r-2$ and $AE = 7.5$. From this, we can solve for $r-1$.$

jathu123 · Jan 16, 2017

You can use the product of intercepts of intersecting chords theorem. Basically, CE*EF=AE*EB. Since CD bisects AB, AE=EB=7.5. Hence, CE*2=7.5^2
--> CE=7.5^2/2 = 28.125 cm

Circle Geo Question (1 Viewer)

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