MathDB

Let

ABCD

be a quadrilateral inscribed in a circle of radius

AB

such that BC \equal{} a, CD \equal{} b, DA \equal{} \frac{3 \sqrt{3} \minus{} 1}{2} \cdot a For each point

M

on the semicircle with radius

AB

not containing

C

and

D,

denote by

h_1, h_2, h_3

the distances from

M

to the straight lines (sides)

BC, CD,

and

DA.

Find the maximum of h_1 \plus{} h_2 \plus{} h_3.

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