In the triangle ABC AC = BC = 20 inches and AB = 10 inches. Circle is inscribed in the triangle, what is the radius of the circle...see attached...#71

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- Feb 12th 2010, 01:22 PM #1

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- Feb 12th 2010, 01:35 PM #2

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- Feb 12th 2010, 01:40 PM #3

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- Feb 12th 2010, 02:10 PM #4
sketch lines from each vertex to the incenter.

note that the area of the three triangles formed sums to the area of the large triangle ...

$\displaystyle \frac{1}{2}(20)r + \frac{1}{2}(20)r + \frac{1}{2}(10)r = \frac{1}{2}(10)h$

$\displaystyle 25r = 5h$

$\displaystyle r = \frac{h}{5}$

find the height of the triangle from the vertex angle to the base and you can find r

- Feb 12th 2010, 02:16 PM #5

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- Feb 12th 2010, 02:53 PM #6

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- Feb 12th 2010, 04:18 PM #7

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- Feb 13th 2010, 12:39 AM #8
1. You are dealing with 2 right triangles. (see attachment)

2. Grey triangle: $\displaystyle h^2 + 5^2 = 20^2$

3. The right triangle at the top of the grey triangle:

$\displaystyle r^2+15^2 = (h-r)^2$

4. Calculate h from 2. and plug in this term into the equation in 3. Solve for r.

__Spoiler__:

Second attempt: The 2 right triangles are similar. So use proportions:

$\displaystyle \dfrac r{15} = \dfrac5h$

First calculate h, then r using the proportion.