Solve problems finding unknown angles and lengths and prove further results using the circle properties listed above.

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Prove the circle properties – the angle at the centre subtended by an arc of a circle is twice the angle at the circumference subtended by the same arc – an angle in a semicircle is a right angle – angles at the circumference of a circle subtended by the same arc are equal – the alternate segment theorem – the opposite angles of a cyclic quadrilateral are supplementary and its converse – a tangent drawn to a circle is perpendicular to the radius at the point of contact and its converse.