Prove that the two circles drawn on the two equal sides of an isosceles triangle as diameters pass through the mid point of the third side.

Hypotenuse of an isosceles triangle is 10cm. Find other two sides of the triangle

Prove that the tangents drawn to a circle at the two ends of a diameter are parallel.

The figure shows three circles drawn with their centers on each vertex of an equilateral triangle' and passing through the other two vertices. Find the area of the region common to all three.

Prove that the Iine joining the midpoints of the two sides of a triangle is parallel to the third side and half of its length.

In the figure, semicircles are drawn with the sides of a triangles as diameters. Prove that the area of the largest semicircle is the sum of the areas of the smaller ones.

Prove that the angle made by two equal chords drawn from a point on the circle is bisected by the diameter through that point.

In the picture, the perpendicular is drawn from the midpoint of the hypotenuse of a right triangle. to the base. Calculate the length of the third side of the large right triangle and the lengths of all three sides of the small right triangle.

The picture shows the parts of a circle centered at each vertex of an equilateral triangle and passing through the other two vertices. What is the perimeter of this figure?