Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Sample Question Paper 2 Mathematics, Exercise 1: PART A

In figure, $\angle PQR=110°$, where $P, Q$ and $R$ are points on a circle with centre $O$. Find $\angle OPR$.

$PQRS$ is a kite with $PQ=PS$ and $RS=RQ$. Prove that the figure formed by joining the mid-points of the consecutive sides a rectangle.

Three friends walk away from a point in three different directions, such that the path of each is equally inclined to those of the other two. Find the angles, their paths make with each other.

It is given that, $\angle \mathrm{XYZ}=70°$ and $XY$ is produced to point $P$. Draw a figure from the given information, if ray $YQ$ bisects $\angle ZYP$, then find $\angle XYQ$ and reflex $\angle QYP$.

Evaluate ${\left(104\right)}^3$ by using suitable identity.

If $a=\frac{1}{9-4\sqrt{5}}$ and $b=\frac{1}{9+4\sqrt{5}}$, find the values of the following

(i) $a^2+b^2$

(ii) $a^3+b^3$

Show that the diagonals of a parallelogram bisect each other.

Prove that the quadrilateral formed (if possible) by the internal angle bisectors of any quadrilateral is cyclic.