Find in-radius for the given triangle

Find the area, circum-radius and in-radius of the pedal triangle.

The circum radius of an equilateral triangle is 4cm. Find the inner radius of the triangle.

Find the area of the given triangle.

Find tan C in the given triangle

In the given triangle ABC, find AE.

Find the area of the shaded region in the diagram below where the given triangle is isosceles with vertices of base lying on axis of the radius perpendicular to the diameters of the two small semicircles

Each side of a triangle is increased by 10cm.I ratio of the perimeters of the new triangle and the given triangle is 5:4, find the perimeter of the given triangle