Geometry problem for circle

Question

enter image description here

Any tips how to proceed? It's for sure that Ac is the radius but what next?

Well, not only AC, but also AB and BC are radiuses. – Tomas Aug 24 '13 at 17:33 — Tomas, Aug 24 '13 at 17:33

score 7 · Accepted Answer · answered Aug 24 '13 at 17:33

7

Hint: $AC=AB=BC$, hence $ABC$ is an equilateral triangle.

answered Aug 24 '13 at 17:33

Hagen von Eitzen

score 4 · Answer 2 · answered Aug 24 '13 at 17:34

4

Hint: AB and BC are also radii.

answered Aug 24 '13 at 17:34

njguliyev

Parth Thakkar · Answer 3 · 2013-08-24T17:55:12.333

3

Since the circles have the same radius, $$ AC = AB = \text{radius of circle 1} = \text{radius of circle 2} = CA = CB $$

Now consider the triangle $ ACB$.

edited Aug 24 '13 at 17:55

answered Aug 24 '13 at 17:33

Parth Thakkar

No need to say "Assuming"! They have the same radius. – Ted Shifrin Aug 24 '13 at 17:51
I thought of that, and that's quite obvious from the figure and the fact that nothing is said about it - but then...there's always an element of doubt. I mean, that was typed just like that. I'll edit it if you say :D – Parth Thakkar Aug 24 '13 at 17:53
1

I agree one can't assume anything from a figure. But we are told that $A$ and $C$ are the centers, so $\overline{AC}$ is a radius of both circles. :) – Ted Shifrin Aug 24 '13 at 17:55
Ah damn! That I didn't even think. Removing the strikethrough too. Thanks for pointing it out – Parth Thakkar Aug 24 '13 at 17:56

3 Answers3