finding the radius of a circle inscribed in a right triangle

In this video I show how to find the radius of a circle inscribed in a right triangle. This complex geometry problem involves ideas such as Pythagorean Theorem, similar triangles, circle geometry, radius of a circle, tangents drawn to a circle, tangents drawn to a common point.

Write any topics you would like me to cover in the COMMENT section below. THANKS for watching!

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[adlerbrietzke]

Area of the circle inscribed in a right triangle:
r = (a + b - c)/2
Where a and b are base and height or height and base, and c is the hypotenuse
Once the hypotenuse was not given, there was the additional effort to use the pythagorean theorem to solve for the hypotenuse

[rayaanfuaad]

Dude, I'm 15.. I solved it in about 5 second or so, I was pretty much sure I'm wrong.. but I clicked the video and skipped to the end and saw I got the same answer 😁

[sarmabudampati]

If we join the vertices of the triangle with centre of the circle we get three small triangles with each side as base and radius as height.
Now we may equate the area of original triangle=
Sum of areas of three new triangles.
1/2 ×27×36=1/2 × radius × (27+36+45)
27×36 = r ×108
Radius r = 9
This is BSP sarma a retired Bank employee from Hyderabad,
I hope you will appreciate the same.

[rashidissa]

I always argue that if a triangle is right angled, it should be specifically be mentioned. Presumption should be avoided even if it is drawn and looks like it

[triole]

Hi, since the triangle legs are not the same length, are you sure that the line you draw on 1:03 is perpendicular to the hypothenuse/tangent? Imagine a square triangle whose legs would measure 20 and 65 (ex). The hypothenuse wouldn’t be a tangent to the circle in the same point. So it’s perpendicular line wouldn’t be the same.

[genesisanderson]

Great video, all though it was a bit confusing