3 Views

Question : In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other at X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of the chord PQ is:

Option 1: $2\sqrt{13}\;\mathrm{cm}$

Option 2: $5\sqrt{3}\;\mathrm{cm}$

Option 3: $4\sqrt{6}\;\mathrm{cm}$ 

Option 4: $6\sqrt{5}\;\mathrm{cm}$


Team Careers360 25th Jan, 2024
Answer (1)
Team Careers360 26th Jan, 2024

Correct Answer: $4\sqrt{6}\;\mathrm{cm}$


Solution :

We have, $\mathrm{AX:BX = 3:2}$ and the radius of the circle is $5\;\mathrm{cm}$.
$\mathrm{AX=\frac{3}{5} \times 10 = 6}\;\mathrm{cm}$
$\mathrm{BX=\frac{2}{5} \times 10 = 4}\;\mathrm{cm}$
We know the theorem states that the two chords of a circle intersect within the circle, the product of the segments of one chord is equal to the product of the segments of the other chord.
$\mathrm{PX\times QX = AX \times XB}$
$\mathrm{PX^2=6 \times 4}$ [Since $\mathrm{PX =QX}$]
$\mathrm{PX=2\sqrt{6}}$
$\mathrm{PQ=2PX=4\sqrt{6}}$
Hence, the correct answer is $4\sqrt{6}\;\mathrm{cm}$.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books