select the correct answer.
quadrilateral bcde is inscribed in circle a as shown. $\boldsymbol{bd}$ divides the quadrilateral into two triangles, $\triangle bcd$ and $\triangle bed$. which statement is true about the triangles?
$\bigcirc$ a. the angle bisectors and the perpendicular bisectors for both triangles intersect at the same point.
$\bigcirc$ b. the angle bisectors of $\triangle bcd$ intersect at the same point as those of $\triangle bed$
$\bigcirc$ c. the perpendicular bisectors of $\triangle bcd$ intersect at the same point as those of $\triangle bed$.
$\bigcirc$ d. the angle bisectors of $\triangle bcd$ intersect at the same point as the perpendicular bisectors of $\triangle bed$.

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# Answer:
C. The perpendicular bisectors of $	riangle BCD$ intersect at the same point as those of $	riangle BED$.
# Brief Explanations:
The perpendicular bisectors of any triangle inscribed in a circle intersect at the circle's center (the circumcenter). Since both $	riangle BCD$ and $	riangle BED$ are inscribed in circle $A$, their perpendicular bisectors all intersect at point $A$, the center of the circle. Angle bisectors intersect at the incenter, which is unique to each triangle and not the same point here, eliminating the other options.

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