# Two circles with centers A and B touch each other internally. Another circle touches the larger circle externally at the point x and the smaller circle externally at the point y. If O be the centre of that circle, let us prove that AO + BO is constant.

Let the radius of the circle with centre A be Ra, B be Rb and O be Ro

Length OA = Radius of circle O + Radius of circle A

OA = Ro + Ra

Length OB = Radius of circle O + Radius of circle B

OB = Ro + Rb

AO + BO = Ro + Ra + Ro + Rb

AO + BO = 2Ro + Ra + Rb

Since the radius is always a constant quantity so AO + BO is also a constant quantity.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Area Related with the Circle45 mins
Quiz | A Letter to God39 mins
Quiz | Area Related with Circles47 mins
A Letter to God45 mins
A Letter to God50 mins
How to build a strong Vocabulary?53 mins
Time-Management: A key to Success37 mins
Let's Calculate - A Guide to an Economist's Dictionary54 mins
Tricks to MemoriseFREE Class
Smart and Effective study is the Key of success45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses