Magic Crown

Geometry Level pending

The diagram shows a circle with center O O , ∠ D C B = 3 0 ∘ \angle DCB = 30^\circ , and the area of minor sector D O B DOB is 480 480 . By finding the measure of ∠ D O B \angle DOB , find the radius of the circle. Round your answer to the nearest integer.

Credits: Golden Goh

Half-Inscribed


The answer is 30.

Ethan Mandelez by Ethan Mandelez , 15, Malaysia

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2 solutions

Angle \textrm{Angle } D O B = 2 × 30 ° = 60 ° = π 3 DOB = 2×30°=60°=\frac{π}{3}

Area \textrm{Area} = π / 3 2 π × π r 2 = 480 \frac{π/3}{2π}×πr^2 = 480 r = 6 80 π r= 6\sqrt{\frac{80}{π}} r = 30.277 r = 30.277 Answer is \textrm{Answer is} r = 30 unit \boxed{r=30} \textrm{ unit}

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Ethan Mandelez
Dec 3, 2020

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