Condition for Perpendicularity of Two Straight Lines

Q. Let $PQ$ and $RS$ be tangents at the extremities of the diameter $PR$ of a circle of radius $r$. If $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle, then $2r$ equals

1. $\frac{PQ+RS}{2}$
2. $\sqrt{PQ\times RS}$
3. $\frac{2PQ\times RS}{PQ+RS}$
4. $\frac{\sqrt{(P{Q}^2+R{S}^2)}}{2}$

Q. A line $y=mx+1$ intersects the circle $(x-3{)}^2+(y+2{)}^2=25$ at the points $P$ and $Q$. If the midpoint of the line segment $PQ$ has $x$-coordinate $-\frac{3}{5}$, then which one of the following options is correct?

1. $-3\le m<-1$
2. $2\le m<4$
3. $4\le m<6$
4. $6\le m<8$

Q. Let $PQ$ and $RS$ be tangents at the extremities of the diameter $PR$ of a circle of radius $r$. If $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle, then $2r$ equals

1. $\sqrt{PQ\times RS}$
2. $\frac{PQ+RS}{2}$
3. $\frac{2PQ\times RS}{PQ+RS}$
4. $\frac{\sqrt{(P{Q}^2+R{S}^2)}}{2}$