SOLUTION: A right triangle is inscribed in a circle with radius 26cm. If the length of one of the legs of this triangle is 20 cm, find the difference between the area of the circle in which

Algebra ->  Pythagorean-theorem -> SOLUTION: A right triangle is inscribed in a circle with radius 26cm. If the length of one of the legs of this triangle is 20 cm, find the difference between the area of the circle in which       Log On


   

Question 1018157: A right triangle is inscribed in a circle with radius 26cm. If the length of one of the legs of this triangle is 20 cm, find the difference between the area of the circle in which the triangle is inscribed and the area of the inscribed circle. Express your answer in terms of pi.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The inscribed triangle is a right triangle, and the longest side, its hypotenuse, is a diameter of the circle, 52 cm.

u, the unknown leg:
u%5E2%2B20%5E2=52%5E2 according to Pythagorean Theorem Formula;
u%5E2=52%5E2-400
u%5E2=2304
u%5E2=576%2A4=288%2A2%2A4=144%2A2%2A2%2A4
u%5E2=12%2A12%2A4%2A4
highlight%28u=48%29

The 90-degree angle of the triangle is between u=48, and 20 cm leg.

If you want the area of the inscribed triangle by itself, then highlight%28%281%2F2%29%2A48%2A20=highlight%28480%29%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A right triangle is inscribed in a circle with radius 26cm. If the length of one of the legs of this triangle is 20 cm, find the difference between the area of the circle in which the triangle is inscribed and the area of the inscribed circle. Express your answer in terms of pi.
Difference between areas of circle and inscribed triangle: