Tangential Paradox

Geometry Level 2

In a rectangle two semicircles touches each other and a tangent to two semicircles is drawn intersecting breath of the rectangle as shown. What fraction of the rectangle is yellow?

Note: it's not given that width is bisected.

⅔ ⅘ ¾ ½

Swaroop Dora by Swaroop Dora , 22, India

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1 solution

The word 'intersecting' should actually be ' bisecting '. Let the length of the rectangle be a a and it's breadth be b b . Then the area of the rectangle is a b ab , that of the white triangle is 1 2 × b 2 × a = 1 4 a b \dfrac{1}{2}\times \dfrac{b}{2}\times a=\dfrac{1}{4}ab and of the yellow trapezium is ( 1 − 1 4 ) a b \left (1-\dfrac{1}{4}\right) ab . Hence the required fraction is 3 4 \boxed {\dfrac{3}{4}} .

1 Helpful 0 Interesting 0 Brilliant 1 Confused

Wrong solution and assuming that its bisecting

Swaroop Dora - 1 year, 2 months ago

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