Three tangent circles.

Geometry Level 2

In the figure shown the radius of the largest orange circle a is 16 cm and that of the smallest green circle c is 9 cm

What is the radius of the white circle b in the middle ?


The answer is 12.

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1 solution

r is the radius of the middle circle. Draw a line parallel to the line of centers through ’ a ’ the tangency point of the small circle to cut the middle radius at ’ e ’ and the big radius at ’ d.’ ’abd’ is the triangle with ’ be ’ in middle circle parallel to ’ cd ’ S o 25 + 2 r 7 = 9 + r r 9 2 r 2 = 288 r = 12 \text{r is the radius of the middle circle.}\\ \text{Draw a line parallel to the line of centers through ' a ' the tangency point} \\\text{of the small circle to cut the middle radius at ' e ' and the big radius at ' d.'} \\ \text{'abd' is the triangle with ' be ' in middle circle parallel to ' cd '} \\So~\dfrac{25+2r}{7}\\=\dfrac{9+r}{r-9}\\2r^2=288~~\implies~~~r=~~\color{#D61F06}{\boxed{12} }

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