MathDB

An acute isosceles triangle,

ABC

is inscribed in a circle. Through

B

and

C

, tangents to the circle are drawn, meeting at point

D

. If

\angle ABC=\angle ACB=2\angle D

and

x

is the radian measure of

\angle A

, then

x=

[asy] defaultpen(linewidth(0.7)+fontsize(10)); real x=180/7; pair D=origin, B=dir(3x), C=dir(4x), A=intersectionpoint(C--C+dir(2x), B--B+dir(5x)), O=circumcenter(A,B,C); markscalefactor=0.015; draw(B--C--D--B--A--C^^Circle(O, abs(O-C))^^anglemark(C,A,B)); dot(A^^B^^C^^D); pair point=O; label("

A

", A, dir(point--A)); label("

B

", B, dir(point--B)); label("

C

", C, dir(point--C)); label("

D

", D, dir(point--D)); label("

x

", A+0.1*dir(270), S);[/asy]

\text{(A)} \ \frac37\pi \qquad \text{(B)} \ \frac49\pi \qquad \text{(C)} \ \frac5{11}\pi \qquad \text{(D)} \ \frac6{13}\pi \qquad \text{(E)} \ \frac7{15}\pi

Problem Statement