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The ratio of the length of de and the length of bc @mylittlestar

The ratio of the length of de and the length of bc @mylittlestar-example-1
User KrauseFx
by
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7 votes

Answer:

The ratio of the length of DE and the length of BC = 1/4

Explanation:

From the figure we can see two sectors

To find the length of BC

The sector ABC with radius r and central angle 2β

BC = (2πr)( 2β/360)

= 4πrβ/360

To find the length of DE

The sector ADE with radius r/2 and central angle β

DE = (2πr/2)( β/360)

= πrβ/360

To find the ratio of DE to BC

DE/BC =πrβ/360 ÷ 4πrβ/360

= πrβ/360 * 360/ 4πrβ

=1/4

User Tibor Nagy
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