(a) \( \ \ \) Show that \( \angle DSR = \angle DAR \). The quadrilateral \( DRAS \) is cyclic, since \( \angle DRA + \angle DSA = \pi (180^{\circ}) \). Therefore \( \angle DSR = \angle DAR \) (angles in the same segment of circle \( DRAS \), both standing on same chord […]

# Tag Archives: Circle Geometry

# Cyclic Quadrilateral in Circle Geometry

A cyclic quadrilateral is inscribed into a circle, whose vertices all lie on a circle. The properties of cyclic quadrilateral in circle geometry are; Opposite angles in a cyclic quadrilateral supplementary. Exterior angle and its opposite angle are equal. (a) Prove that \( FADG \) is a cyclic quadrilateral. \( \begin{aligned} \require{color}\text{Let } \angle BCD […]

# Circle Geometry with Semicircles

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 […]