Question

Two circles of same radii r and centres O and O' touch each other at P as shown in Fig. 10.91. If 00' is produced to meet the circle C (O', r) at A and AT is a tangent to the circle C(O, r) such that O'Q ⊥ AT. Then AO: AO' =
A. 3/2
B. 2
C. 3
D. 1/4

Answer 1

To calculate the ratio of AO : AO’ we have to keep in mind that the circles have the same measure of the radius, as it is given in the question.

Explanation:

So, before we jump to the solution part, there are a few things that we have to keep in mind.

(1) The circles have the same radius.

(2) The tangent part in the question is only given to confuse.

We totally try and focus on what’s given here.

‘r’ is the radius of the circles.

So, by looking at the figure, we can tell that –  

OP = PO’ = O’A = r. [ they measure same……given].

And AO = AO’ + O’P + PO.

But as AO’ = O’P = PO = r (given),

So, we can also say that AO = r + r +r.

  AO = 3r.

Also, AO’ = r.

So AO: AO’ = 3r : r

Or, AO/AO' = 3r/r   (as r is common in both numerator and denominator, so we can cancel ‘r’).

Or AO/AO'  = 3/1

Or, AO: AO’ = 3: 1 = 3.

So the correct answer here has to be option 3.