Googly Eyes

Geometry Level 3

In the figure above, the value of $\overline{AB} = 8$ , find the radius of the circle $C_2$ .

\frac{\pi}{3}

\frac{5}{7} \sqrt{2}

\frac{4}{7} \sqrt{3}

2 \sqrt{2} - 1

\frac{1}{2}

1

2 solutions

Ahmad Saad
Jun 18, 2016

Martin Gray
Jun 22, 2016

Let O1 be centre of C1, O2 be centre of C2, D be point where C2 touches largest circle, r be radius of circle C2.

Line OD = radius of large circle = 4. Line OO2 = 4-r. Line O1O2 = 2+r. Lines OO2 and O1O2 form two sides of an isosceles triangle with base OO1 and are therefore the same.

Solve 4-r = 2+r for r gives r=1

Excuse format, done on iPhone :-)

Googly Eyes

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