Thread: sss or sas ?

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

Where are you stuck?

well i'm pretty sure the one radius pointing down is the midpoint of AB so those 2 segments are 5 inches, then i bisected the 3 angles in the circle to figure out that Ar and Br should be 5 inches each. i dont know what to do next

Originally Posted by igottaquestion

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

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 ...







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

ok so the height is 5 sq rt of 15, so r=sq rt of 15?

That's it!

Well...let equal sides = a and base = b

radius incircle = bSQRT(4a^2 - b^2) / [2(2a + b)]

OR (if you prefer the SQRT in denominator!):

radius incircle = b(2a - b) / [2SQRT(4a^2 - b^2)]

No need to calculate height.

Originally Posted by igottaquestion

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

1. You are dealing with 2 right triangles. (see attachment)

2. Grey triangle:

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



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

Spoiler:

You should come out with

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



First calculate h, then r using the proportion.