Express sec A and cos A in terms of sides of right angle triangle

The circum radius of a right angled triangle is

Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

Express the following angles in terms of a right angle . 60^@

Somen has drawn a right-angled triangle, the hypotenuse of which is 3 cm more the twice of its smallest side. If the length of its third side be 1 cm less than the hypotenuse, then find the lengths of the sides of the right-angled triangle.

Prove that if equilateral triangles are drawn on the sides of a right-angled triangles then the area of the equilateral triangle, drawn on the hypotenuse is equal to the sum of the areas of the other two equilateral triangals drawn on its other two sides.

The perpendicular bisector of the three sides of a right - angled triangle intersect each other

If the sum of the lengths of the hypotenuse and another side of a right-angled triangle is given, show that the area of the triangle is maximum when the angle between these sides is pi/3dot

The length of hypotenuse and one side of a right -angle triangle are [3+2 (sin theta+ cos theta)] and [2(1+ sin theta)+cos theta)] respectively, show that the lengths of the other side of the triangle is [ 2(1+cos theta)+ sin theta]

Lets find, if the statement given below are correct or not (a) Hypotenuse in the smallest side of a right angled triangle.

A point D is taken from the side BC of a right angled triangle ABC, where AB is hypotensuse. Then___