MHT CET · Maths · Circle
Two tangents drawn from \(\mathrm{P}(1,7)\) to the circle \(x^2+y^2=25\), touch the circle at Q and R respectively. The area of the quadrilateral PQOR is
- A 16 sq. units
- B 36 sq. units
- C 25 sq. units
- D 49 sq. units
Answer & Solution
Correct Answer
(C) 25 sq. units
Step-by-step Solution
Detailed explanation
Length of tangent segment from \(\mathrm{P}(1,7)\) is
\(\begin{aligned}
\sqrt{1^2+7^2-5^2} & =5 \\
\text { Required area } & =2 \times \text { Area of } \triangle \mathrm{PQO} \\
& =2 \times \frac{1}{2} \times 5 \times 5 \\
& =25 \text { sq. }
\end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If line \(x+y=0\) touches the curve \(a x^{2}=2 y^{2}-b\) at \((1,-1)\),
then the values of \(a\) and \(b\) are respectivelyMHT CET 2020 Easy - The equation of the plane containing the line \(\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}\) and the point \((0,7,-7)\) isMHT CET 2008 Easy
- \(\cos ^2 48^{\circ}-\sin ^2 12^{\circ}=\) __________ , if \(\sin 18^{\circ}=\frac{\sqrt{5}-1}{4}\)MHT CET 2023 Easy
- If \(\cos 2 \theta=\sin \propto, \quad\) then \(\theta=\)MHT CET 2020 Easy
- Mean and variance of six observations are 6 and 12 respectively. If each observation is multiplied by 3 , then new variance of the resulting observations isMHT CET 2024 Medium
- If one of the lines given by \(k x^{2}+x y-y^{2}=0\) bisects the angle between the co-ordinate axes, then values of \(k\) areMHT CET 2020 Medium
More PYQs from MHT CET
- The slant height of a right circular cone is \(3 \mathrm{~cm}\). The height of the cone for maximum volume isMHT CET 2021 Hard
- A coil of wire of radius ' \(r\) ' has 600 turns and a self-inductance of 108 mH . The self-inductance of a coil with same radius and 500 turns isMHT CET 2025 Easy
- A simple pendulum has a periodic time ' \(\mathrm{T}_1\) ' when it is on the surface of earth of radius ' \(R\) '. Its periodic time is ' \(T_2\) ' when it is taken to a height ' \(R\) ' above the earth's surface. The value of \(\frac{T_2}{T_1}\) isMHT CET 2024 Medium
- Angles of a triangle are in the ratio \(4: 1: 1\). Then the ratio of its greatest side to its perimeter isMHT CET 2023 Easy
- Three vectors are expressed as \(\vec{a}=4 \hat{i}-\hat{j}, \vec{b}=-3 \hat{i}+2 \hat{j}\) and \(\vec{c}=-\hat{k}\). The unit vector along the direction of sum of these vectors isMHT CET 2025 Easy
- Decrease and increase in the number of RBCs is respectively termed asMHT CET 2019 Easy