25 Views

Question : Two circles of radii 12 cm and 13 cm are concentric. The length of the chord of the larger circle which touches the smaller circle is:

Option 1: 8 cm

Option 2: 18 cm

Option 3: 10 cm

Option 4: 12 cm


Team Careers360 24th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: 10 cm


Solution :
Let O be the centre of the circle. OA = 13 cm and OM = 12 cm.
Let AB be the chord of the smaller circle which is tangent to a smaller circle.
Since the tangent is perpendicular to the radius at its point of contact, angle OMA is a right angle.
By Pythagoras theorem,
OA 2 = AM 2 + OM 2
⇒ 13 2 = AM 2 + 12 2
⇒ AM 2 = 25
⇒ AM = 5 cm
Also, perpendicular from the centre to a chord bisects the chord.
AB = 2 × AM = 2 × 5 = 10 cm
Hence, the correct answer is 10 cm.

How to crack SSC CHSL

Candidates can download this e-book to give a boost to thier preparation.

Download Now

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