# What are the circle theorems

what r the circle theorems
0%

Circle Theorems:
1. The angle at the centre of a circle is twice the angle at the circumference subtended by the same arc.
2. Angles in the same segment of a circle are equal.
3. The angle subtended by a diameter at the circumference is equal to a right angle (90◦)
4. The opposite angles of a quadrilateral inscribed in a circle sum to two right angles (180◦). (The opposite angles of a cyclic quadrilateral are supplementary). The converse of this result also holds.
5. A tangent to a circle is perpendicular to the radius drawn to the point of contact.
6. The two tangents drawn from an external point to a circle are of the same length.
7. The angle between a tangent and a chord drawn from the point of contact is equal to any angle in the alternate segment.
8. If AB and CD are two chords which cut at a point P (which may be inside or outside the circle) then PA · PB = PC · PD.
9. If P is a point outside a circle and T, A, B are points on the circle such that PT is a tangent and PAB is a secant then PT^2 = PA · PB
These theorems are better understood with pictorial examples. Have a look at: https://www.docsity.com/en/circle-definitions-and-theorems-handout-mathematics/900083/