Exercise

Three vertices of a parallelogram are $P(-2, 2), Q(6, 2)$ and $R(4, -3)$. Plot these points on a graph paper and hence, use it to find the coordinates of the fourth vertex $S$. Also, find the coordinates of the midpoint of the side $RS$. What is the area of the parallelogram?

In the below-given figure, $ABC$ is an equilateral triangle. Find the coordinates of the vertices.

In the below given figure, $O$ is the centre and $AOE$ is the diameter of the semicircle. If $AB=BC$ and $\angle OEC=50°$. Find $\angle AOB$

Prove that $OB$ is parallel to $EC$

In the following figure, find the point identify the coordinate $\left(-5, 3\right)$.

In an experiment a thin beam of light is made to enter a water drop of diameter 2 mm. The ray of light, after internal reflection, exit out of the water drop. It was determined that the distance of path of light within the water drop was 0.5 mm away from the centre.

Estimate the distance travelled by the light within the water drop.

Point $O$ is the centre of the circle.

If $BC= CD= DE$, then find $\angle ABE$.

In the figure below $∆ABC$ is an equilateral triangle. Bisector of $\angle B$ intersects circumcircle of $∆ABC$ in point $P.$ Prove that, $CQ=CA$

If the vertex of an angle $ABC$ be located outside a circle and the sides of the angles intersects equal chords $AD\text{ and} CE$ with the circle, then prove that $\angle ABC$ is equal to half the difference of the angles subtended by the chords $AC\text{ and }DE$ at the centre.