There are many properties of circle geometry with semi circles, such as

- equal arcs on circles of equal radii subtend equal angles at the centres equal angles at the centre stand on equal chords
- the angles at the centre is twice an angle at the circumference subtended ay the same arc
- the perpendicular from the centre of a circle to a chord bisects the chord
- equal chords in equal circles are equidistant from the centres
- angles in the same segment are equal
- the angle in a semi-circle is a right angle
- opposite angles of a cyclic quadrilateral are supplementary

### Worked Example of Circle Geometry with Semi Circles

(a) Explain why \( CTDS \) is a rectangle.

(b) Show that \( \triangle MXS \) and \( \triangle MXC \) are congruent.

(c) Show that the line \( ST \) is a tangent to the semicircle with diameter \( AC \).

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