What Acute Angle You Have There!

Geometry Level 4

ABCABC is an acute triangle with BCA=35 \angle BCA = 35 ^\circ. Denote the circumcenter of ABCABC as OO and the orthocenter of ABCABC as HH. If AO=AHAO=AH, what is the value of ABC\angle ABC (in degrees)?

Details and assumptions

The circumcenter of a triangle is the center of a circle which passes through all three vertices of a triangle.
The orthocenter of a triangle is the intersection of the 3 altitudes (perpendicular from vertices to opposite side).

You may choose to read this page on extended sine rule.


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