If the points P , Q, R and S are collinear points and PQ=RS then prove that PR=QS using Euclid’s postulate.

Q. If P, Q and R are three collinear points such that $\overrightarrow{PQ}=\overrightarrow{a}$ and $\overrightarrow{QR}=\overrightarrow{b}$. Find the vector $\overrightarrow{PR}$.

Q. Question 12
If S is a point on the side PQ of a $\Delta$ PQR such that PS = QS = RS, then

$\left(A\right)\left(PR\right)\left(QR\right)=R{S}^2$
$\left(B\right)Q{S}^2+R{S}^2=Q{R}^2$
$\left(C\right)P{R}^2+Q{R}^2=P{Q}^2$
$\left(D\right)P{S}^2+R{S}^2=P{R}^2$

Q. If a point $Q$ lies between two points $P$ and $R$ such that $PQ=QR$, prove that $PQ=\frac{1}{2}PR$

Q. If a line intersect two concentric circles with centre A in points P,Q, R and S respectively then prove that PQ = RS. (Fig.4.35)

Q. In a $\Delta PRS,\angle PRS={120}^o$. A point $Q$ is taken of $PR$ such that $PQ=QS$ and $QR=RS$ then $\angle QPS=....$