LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
3.4k views
in Circles by (23.8k points)
closed by

If a line l intersects two concentric circles at points A, B, C, and D as shown in the figure, prove that AB = CD. 

OR 

Prove that two concentric circles intercept equal portions on any straight line that cuts them.

1 Answer

+1 vote
by (24.6k points)
selected by
 
Best answer

Let O be the centre of the two concentric circles and OM the perpendicular from O to the line l. AD is the chord of the larger circle and BC, the chord of the smaller circle.

Since, perpendicular from the centre to a chord bisects the chord, therefore, 

AM = MD ...(i) 

and BM = MC ...(ii)

 (i) and (ii) gives, AM – BM = MD – MC 

AB = CD.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...