The first original geometry problem in 2015!
It is given a triangle with and and a point in the interior, for which and What is the measure in (degrees) of
NOTE: This problem is original!
The answer is 86.
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1 solution
By Trigonometric Form of Ceva's Theorem:
sin ( 4 ) sin ( 3 0 ) sin ( x ) sin ( 1 1 2 − x ) sin ( 2 6 ) sin ( 8 ) = 1 ⇒ x = 8 6 ⇒ ∠ M C B = 8 6
Solution 2
Triangle ABC can be constructed inside an equilateral triangle ABC' with point M as a vertex of a smaller equilateral triangle positioned at the center of the triangle ABC'. The angle measures match the requirements stated in the problem and the unknown angle can be easily computed.