Question

Find the radius of the circle inscribed in a triangle abc. triangle abc is a right-angled isosceles triangle with the hypotenuse as 62√

Answer 1

To solve this problem we will have to make use of an important property of a right triangle inscribed in the circle. That property states that: "The hypotenuse of a right triangle inscribed in a circle is always the diameter of the circle."

Thus, if we know the value of the hypotenuse of a right triangle inscribed in a circle, then we will know that value of the diameter of the same circle as hypotenuse and diameter will be be the same.

In our case, we are given that the hypotenuse is $\sqrt{62}$.

Therefore, the diameter too will be $\sqrt{62}$.

Thus, the radius of the circle will be: $\frac{\sqrt{62} }{2}$, which is the required answer.

Answer 2

Hypotenuse is 6 root 2 cm.

The sides for this will be 6 cm because it is an isosceles triangle.

2/3 rd of the length of sides that is 2 / 3 * 6 = 4cm

Now if the radius of the triangle will be dropped or reduced it will be become the perpendicular on sides.

Now it will form a square: with a side of 2 cm each ((6-4)=2)

So the radius of the circle is 2 cm.