In this sub-topic, we will discuss some important circle theorems. We will also learn to apply these theorems to solve different types of mathematical problems involving circle.

Theorem 1:

The perpendicular from the canter of a circle to a chord bisects the chord. In other words, the perpendicular bisector of a chord passes through the canter of the circle.

Theorem 2:

Equal chords of a circle are equidistant from the center.

Theorem 3:

When two circles intersect each other, then the line joining their centers bisects their common chord at right angles.

Theorem 4:

Products of intercepts of two intersecting chords are equal.
In Figure 14, AP × PB = CP × PD.

When an angle is on a circle, the vertex is on the circumference of the circle. One type of angle on a circle is the inscribed angle, from the previous section.

A central angle of a circle is an angle whose vertex is the center of the circle and whose sides are radii of the circle.