CIRCLE GEOMETRY ​

You should be able to

 

solve geometric problems using properties of circles and circle theorems.

 

The angle which an arc of a circle subtends at the centre of a circle is twice the angle it subtends at any point on the remaining part of the circumference. The angle in a semicircle is a right angle. Angles in the same segment of a circle and subtended by the same arc are equal. The opposite angles of a cyclic quadrilateral are supplementary. The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle. A tangent of a circle is perpendicular to the radius of that circle at the point of contact. The lengths of two tangents from an external point to the points of contact on the circle are equal. The angle between a tangent to a circle and a chord through the point of contact is equal to the angle in the alternate segment. The line joining the centre of a circle to the midpoint of a chord is

 

 

Circle Theorem