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SAT® Math

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Difficult

A Sector with Two Unknowns

SATMAT-JJTJRZ

Created for Albert.io. Copyright 2016. All rights reserved.

Segment $AE$ is a diameter of circle $C$ in the figure above.

If segment $DB$ is tangent to circle $C$ at point $B$, the measure of angle $D$ is $ { 24 }^{ \circ } $, $AD=11$ units, and $DB=17$ units, then what is the area of the shaded sector bounded by points $B$, $C$, and $E$ ? (No Calculator)

A

About $ 51 \text{ units}^2$

B

About $ 54 \text{ units}^2$

C

About $ 58 \text{ units}^2$

D

About $ 61 \text{ units}^2$