Collinear Proof in Circle Geometry

(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 […]

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 […]