MathDB

Let

ABC

be a triangle with

\angle A=105^o

and

\angle C=\frac{1}{4} \angle B

. a) Find the angles

\angle B

and

\angle C

b) Let

O

be the center of the circumscribed circle of the triangle

ABC

and let

BD

be a diameter of that circle. Prove that the distance of point

C

from the line

BD

is equal to

\frac{BD}{4}

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