In the circle given below,let OA=1 unit, OB=13 unit and PQ\perp OB. Then, the area of the triangle PQB (in square units ) is :
 
Option: 1 26\sqrt{2}
Option: 2 26\sqrt{3}
Option: 3 24\sqrt{2}  
Option: 4 24\sqrt{3}

Answers (1)

To solve this concept, we will use two concepts that we have learnt in class 9 or 10.

The perpendicular from the centre of a circle to a chord bisects the chord.

If two chords of a circle intersect each other, then the products of the lengths of their segments are equal.

PQ and OB are the chords of the circle

PQ\perp OB

Given OA = 1 unit, OB = 13 unit, so, AB = 12 unit

\text{Let PA = AQ }=\lambda

\\\mathrm{OA\cdot OB =PA\cdot AQ}\\\Rightarrow 1\times 12=\lambda\times \lambda\\\Rightarrow \lambda=2\sqrt3\\

\\\text { Area } \Delta \mathrm{PQB}=\frac{1}{2} \times 2 \lambda \times \mathrm{AB} \\ \Delta=\frac{1}{2} \cdot 4 \sqrt{3} \times 12 \\ =24 \sqrt{3}

Most Viewed Questions

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 14999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions