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

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.

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.

At two ends of a horizontal line, angles of equal size are drawn, and two points on the slanted lines are joined. Prove that the two slanted lines at the ends of the horizontal line are in the same ratio

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.

In the figure, squareP=90^o . Sides of triangle APC are extended to B and D. Prove that, the circles drawn with the sides of a quadrilateral with perpendicular diagonals, will meet at a common point. .

The picture shows a triangle formed by three tangents to a circle. . Calculate the length of each tangent from the corner of the triangle to the point of contact.

What sort of a quadrilateral is formed by the tangents at the ends of two perpendicular diameters of a circle?

In the picture a triangle is formed by two mutually perpendicular tangents to a circle and a third tangent. Prove that the perimeter of the triangle is equal to the diameter of the circle.

The picture shows the tangents at two points on a circle and the radii through the points of contact. Prove that the tangents have the same length.