My Math Forum find radius of the circle

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August 25th, 2018, 03:47 AM   #1
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 August 25th, 2018, 06:14 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,973 Thanks: 2223 You'll need some further information or assumptions. For example, can you assume that AB is a tangent to the circle at B? Even if you can, you'll need some further information.
August 25th, 2018, 07:26 AM   #3
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Yes, it seems that result isn't unique with given inputs.
(See pictures.)

In spite of that, it can be shown that $\displaystyle \triangle ABD \sim \triangle ABC$, $\displaystyle AC=18 cm$, $\displaystyle DC=10 cm$ and $\displaystyle \frac{BC}{BD}=\frac{3}{2}$.
To find $\displaystyle r$ (using the law of sines, for example), it is necessary to provide more data.
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Last edited by lua; August 25th, 2018 at 07:35 AM.

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