- The angle at the centre of a circle is twice the angle at the circumference subtended by the same arc.
- Angles in the same segment of a circle are equal.
- The angle subtended by a diameter at the circumference is equal to a right angle (90◦)
- 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.
- A tangent to a circle is perpendicular to the radius drawn to the point of contact.
- The two tangents drawn from an external point to a circle are of the same length.
- The angle between a tangent and a chord drawn from the point of contact is equal to any angle in the alternate segment.
- 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.
- 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/
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