Andhra Pradesh Board Solutions for Chapter: Circles, Exercise 8: EXERCISE - 12.5

Given that the vertices $\mathrm{A},\mathrm{B},\mathrm{C}$ of a quadrilateral $\mathrm{ABCD}$ lie on a circle. Also $\angle \mathrm{A}+\angle \mathrm{C}=180°$, then prove that the vertex $\mathrm{D}$ also lie on the same circle.

Prove that a cyclic rhombus is a square.

For a rectangle draw a circle and inscribe the figure given. If a polygon of the given type can't be inscribed, write not possible.

For a trapezium draw a circle and inscribe the figure given. If a polygon of the given type can't be inscribed, write not possible.

For an obtuse triangle draw a circle and inscribe the figure given. If a polygon of the given type can't be inscribed, write not possible.

For a non-rectangular parallelogram draw a circle and inscribe the figure given. If a polygon of the given type can't be inscribed, write not possible.

For an acute isosceles triangle draw a circle and inscribe the figure given. If a polygon of the given type can't be inscribed, write not possible.

For a quadrilateral $PQRS$ with $\overline{PR}$ as diameter draw a circle and inscribe the figure given. If a polygon of the given type can't be inscribed, write not possible.