Kerala Board Solutions for Chapter: Circles, Exercise 2: Exercise 2

In the picture given below, $O$ is the centre of the circle and $A, B, C$ are points on it. Calculate all angles of $\Delta ABC$ and $\Delta OBC$.

In the picture given below, $O$ is the centre of the circle and $A, B, C$ are points on it. Calculate all angles of $\Delta ABC$ and $\Delta OAC$.

In the picture given below, $O$ is the centre of the circle and $A, B, C$ are points on it. Calculate all angles of $\Delta ABC$ and $\Delta OAC$.

The numbers $1,4,8$ on a clock’s face are joined to make a triangle, in the figure of a clock given below, How many equilateral triangles can we make by joining numbers on the clock’s face?

In the picture, bisectors of adjacent angles of the quadrilateral $ABCD$ intersect at $P, Q, R, S.$ Prove that $PQRS$ is a cyclic quadrilateral.

Draw a triangle of circumradius $3 \mathrm{cm}$ and two of the angles$32\frac{1°}{2}$ and $37\frac{1°}{2}$

In the given figure, $\mathrm{AB}$ and $\mathrm{CD}$ are mutually perpendicular chords of the circle. Prove that the arcs $\mathrm{APC}$ and $\mathrm{BQD}$ joined together would make half the circle.

In the figure given below, $\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D}$ are points on a circle centred at $\mathrm{O}$. The lines $\mathrm{AC}$ and  $\mathrm{BD}$ are extended to meet at P. The line $\mathrm{AD}$ and BC intersect at $\mathrm{Q}$. Prove that the angle which the small arc $\mathrm{AB}$ makes at $\mathrm{O}$ is the sum of the angles it makes at $\mathrm{P}$ and $\mathrm{Q}$.