Home
Class 12
MATHS
A circle touches the hypotenuse of a rig...

A circle touches the hypotenuse of a right angled triangle at its middle point and passes through the mid-point of the shorter side. If `a and b (altb)` be the lengths of the sides, then prove that the radius of the circle is `b/(4a) sqrt(a^2 + b^2)`

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that the mid-point of the hypotenuse of right angled triangle is equidistant from its vertices.

Prove that the mid-point of the hypotenuse of right angled triangle is equidistant from its vertices.

Prove that the mid-point of the hypotenuse of right angled triangle is equidistant from its vertices.

Prove using similar triangles, that a line drawn through the mid-point of one side of a triangle parallel to another side, bisects the third side.

The line drawn through the mid-point of one side of a triangle, parallel to another side, intersects the third side at its mid-point.

A circle touches two of the smaller sides of a DeltaABC(a lt b lt c) and has its centre on the greater side. Then, find the radius of the circle.

The hypotenuse of a right angled triangle has its ends at the points (1," "3) and (" "4," "1) . Find the equation of the legs (perpendicular sides) of the triangle.

The hypotenuse of a right angled triangle has its ends at the points (1," "3) and (" "-4," "1) . Find the equation of the legs (perpendicular sides) of the triangle.

Prove that the mid-point of the hypotenuse of a right triangle is equidistant from its vertices.