Triangle circlesThe circle inside
Name: Date:
Each circle just touches all three sides. Find its radius.
1 cm
2 cm
3 cm
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5 cm
6 cm
Inscribed circle of a triangle worksheets
The circle inside a right triangle touches all three sides at once, and its radius comes out of the three side lengths with no area calculation at all: r = (a + b − c) ÷ 2. These free printable worksheets drill it.
If they get stuck
Inscribed circle of a triangle
The answer key prints on a separate page.
What's on this sheet
The formula looks arbitrary until you walk the tangent lengths. From the right-angle corner, the distance along each leg to where the circle touches is exactly r — that corner and the two touch points make a little square. What is left of the two legs, a − r and b − r, reaches the far corners, and from any corner the two touching lengths are equal, so those two pieces together are exactly the hypotenuse. Rearranged: a + b − c = 2r.
Why this sheet works
Every answer here is a whole number, and that is a property rather than a convenience: a + b − c is even for every Pythagorean triple, so the inradius of a right triangle with whole sides is always whole. The companion sheet asks for the circle through the corners instead, where the same triangle gives a radius that is often a half.
How this one works
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Inscribed circle of a triangle, step by step