# Area Problem #7

If the area of the right angled triangle is 60cm2, find the area of the circle.

## 10 thoughts on “Area Problem #7”

1. Which is absolutely correct! Well done. There’s a direct relationship between the radius of the circle and triangle, regardless of dimensions. r = (a + b + c) / 2

2. Hi

I have solved this to get r=20 by finding the equation of the radius crossing the hypotenuse at right angles in terms of r. Then finding where they intersect again in terms of r and finally using pythagoras to get a quadratic in terms of r. Is there a simpler method?

• I found all 3 sides of the triangle first, then drew a square from the centre of the circle to the top tangent and right angled point of the triangle. You can then get two simple equations using a combination of r a b and c, then solve for r. Your answer is correct.

3. Forgive my stupidity but I can’t visualise where the square is going

4. GeoChatt says:

Neat problem. Would you post a full work up of the solution?

5. A solution that is mostly definitions. Label the points of intersection (chosen to suit the conclusion, above, that r=(a+b+c)/2 using the sides of the triangle):
* D, A, C: on the top horizontal line,
* C, B, E: on the right vertical line,
* F: the center, and
* G: the triangle’s tangent point with the circle
Define:
* a = BC (15 in the example)
* b = AC (8 in the example)
* c = BC (17 in the example)