Play with circles

Geometry Level 2

Two diameters of a circle of radius 6 are drawn to make a central angle of 60°. A smaller circle is placed inside the bigger circle so that it is tangent to the bigger circle and to both diameters. What is the radius of the smaller circle ?


The answer is 2.

Rahul Paswan by Rahul Paswan , 26, India

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2 solutions

Rahul Paswan
Feb 5, 2015

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Just a thought,

1) Center of small circle lays in the bisector of angle AOB, so we draw the bisector.

2) At T point the intersection of bisector with big circle draw its tangent.

3) Extend the two radius tangent to small circle you must get a equilateral triangle, since the resulting triangle is isosceles and one angle is 60 .

4 ) Our circle is the incircle of the above equilateral triangle, being equilateral its center is also the barycenter and the ortocenter, so radius of small circle must 1/3 of big one .

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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