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Given right-angle triangle $\triangle ABC$$(\angle A=90^o)$, with $BC=10$ and $AC=6$. Circle is tangent to $BC$, goes through $A$ and intersects with $AB$ and $AC$ at the points $E$ and $D$ respectively. Find the length of $DE$.

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I tried to solve this question as follows:

$AB=8$ from Pythagoras.

Since $DA\perp AE$ then $DE$ is diameter of the circle.

After drawing it out accurately, I see that $DE=4.8$, but I don't know how to work this out mathematically. Could you please explain to me how to solve this question?

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  • $\begingroup$ Are Trignometric functions allowed ? $\endgroup$ – Anas Khaled Mar 24 at 15:34
  • $\begingroup$ @AnasKhaled yes, but please don't do something that uses a calculator, as I'm trying to understand how to solve this question, without the use of a calculator $\endgroup$ – Michael Blane Mar 24 at 15:35
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    $\begingroup$ There is insufficient information to determine the length of $DE$. $\endgroup$ – player3236 Mar 24 at 15:45
  • $\begingroup$ Sorry, never mind, trig functions weren't necessary. $\endgroup$ – Anas Khaled Mar 24 at 15:48
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The diagrams below shows that there is simply insufficient information to determine the length of $DE$.

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