Question

The lengths of the two sides forming the right angle of a right-angled triangle are 21 cm and 20 cm. What is the radius
of the circle circumscribing the triangle.​

Answer 1

Answer:

First of all, consider a circle drawn around a right triangle ABC. Let O be the midpoint of the hypotenuse AC.

Since, we know that if a chord subtends a right angle at any point on the circumference, then it should be a diameter of the circle.

Therefore, AC (which subtends a right angle at B) is the diameter of the circumcircle. And O, the midpoint of AC is the centre of the circle.

Now, we can easily say that the radius of the circumcircle is 1/2 (AC).

Also, by Pythagoras theorem, AB²+BC²=AC²

So, AC²=441 + 400=841

or AC = 29 cm.

Therefore the required radius is 29/2 cm = 14.5 cm.