Exercise

Find: $m\widehat{PR}$ and $m\widehat{PRT}$

Given $AB=CD.$ Prove that $AC=DB.$

Given $AC=BD.$ Prove that $AB=CD$

In the figure, $\mathrm{X}, \mathrm{Y}$ are the middle points of the arcs $\mathrm{AB}, \mathrm{AC}$. Prove that $\mathrm{AP}=\mathrm{AQ}.$

Circle $O$ with chords $\mathrm{AB}=\mathrm{BC}=\mathrm{CD}=\mathrm{DE}.$ Prove that $\mathrm{AD}=\mathrm{BE}$. Refer the given figure.

In the given figure $\mathrm{APB}$ and $\mathrm{CQD}$ are two congruent arcs. Prove that $\mathrm{AC}\parallel \mathrm{BD}$.

In the given figure, $\mathrm{ABC}$ is equilateral, $\mathrm{P}$and $\mathrm{S}$ are midpoints of arcs $\mathrm{AB}$ and $\mathrm{AC}$.

Prove that $\mathrm{PQ}=\mathrm{QR}=\mathrm{RS}$.

Each side of a regular hexagon, inscribed in a circle subtends an angle of ${60}^{\circ }$ at the centre and is equals to the radius of the circle. Prove it.