Bigger, but how big? [Circles II]

Geometry Level pending

Is the blue portion's area equal to the red portion's area? Assume that all angles that look perpendicular to be perpendicular, and all arcs that look like part of a circle to be part of a circle.

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2 solutions

Vinayak Srivastava
Jun 1, 2020

Red area $=\pi x^2$

Blue area $\dfrac{\pi (2x)^2}{4}=\dfrac{\pi 4x^2}{4}=\pi x^2$

$\implies$ Red area $=$ Blue area $=\pi x^2$

Thanks as always for trying my question @Vinayak Srivastava !

A Former Brilliant Member - 1 year ago

You're welcome! Nice problem!

Vinayak Srivastava - 1 year ago

Mahdi Raza
Jun 2, 2020

\[ \begin{align} {\color{Red}{A_{\text{Quarter circle}}}} &= \pi x^2 \\ \\ {\color{Blue}{A_{\text{Quarter circle}}}} &= \dfrac{\pi (2x)^2}{4} = \dfrac{4}{4} \cdot \pi x^2 \implies \pi x^2 \\ \\ {{\color{Red}{A_{\text{Quarter circle}}}}} &= {{\color{Blue}{A_{\text{Quarter donut}}}}}

\end{align}\]

Bigger, but how big? [Circles II]

2 solutions

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