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

How many chords can be drawn through 12 point on a circle?

How many chords can be drawn through 15 points on a circle?

How many chords can be drawn through 20 points on a circle?

How many chords can be drawn through 21 points on a circle?

How many chords can be drawn, through 23 points on a circle?

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.

Prove that the lengths of the perpendiculars from any point on the bisector of an angle to the sides are equal.

How many chords can be drawn through 21 points?

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.

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