Let PQ and RS be tangents at the extremities | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the diameter be $PR = 2r$. Since $PQ$ and $RS$ are tangents at $P$ and $R$ respectively,$PQ \perp PR$ and $RS \perp PR$.In $	riangle PXR$,$\a

Vedclass · Accepted Answer

$\sqrt{PQ \cdot RS}$

Vedclass · Answer

(A) Let the diameter be $PR = 2r$. Since $PQ$ and $RS$ are tangents at $P$ and $R$ respectively,$PQ \perp PR$ and $RS \perp PR$.In $	riangle PXR$,$\angle PXR = 90^{\circ}$ because it is an angle in a semicircle.Let $\angle RPX = 	heta$. Then $\angle PRX = 90^{\circ} - 	heta$.In $	riangle PQR$,$\angle PQR = 90^{\circ} - 	heta$ and $\angle PRQ = 90^{\circ}$.Thus,$	an(\angle RPX) = 	an 	heta = \frac{RS}{PR} = \frac{RS}{2r}$.Also,in $	riangle PQR$,$	an(\angle PRQ) = 	an(90^{\circ} - 	heta) = \cot 	heta = \frac{PQ}{PR} = \frac{PQ}{2r}$.Therefore,$	an 	heta = \frac{2r}{PQ}$.Equating the two expressions for $	an 	heta$:$\frac{RS}{2r} = \frac{2r}{PQ} \implies (2r)^2 = PQ \cdot RS \implies 2r = \sqrt{PQ \cdot RS}$.

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

Similar Questions

Three numbers are chosen at random from $1$ to $20$. The probability that they are consecutive is

Match the following and choose the correct answer:-
$(A)$ Implantation $(i)$ Vagina
$(B)$ Capacitation (ii) Ovary
$(C)$ Folliculogenesis (iii) Uterus
$(D)$ Fertilisation (iv) Fallopian tube

$C_2H_6 \stackrel{450^{\circ}C}{\longrightarrow} C_2H_4 + H_2$. The above reaction is called:

If $f(x) = \begin{cases} \frac{\sin(1+[x])}{[x]}, & \text{for } [x] \neq 0 \\ 0, & \text{for } [x] = 0 \end{cases}$ where $[x]$ denotes the greatest integer not exceeding $x$,then $\lim_{x \rightarrow 0^{-}} f(x)$ is equal to

Which complex is most stable?
Where $k_d = \text{Dissociation constant}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module