Understand the problem
Source of the problem
Start with hints
As , hint 1 means that . Hence is the orthocentre of . Let be the circumcenter of and be its incentre. From the information given in the second link of hint 1, we see that are colinear.Also, as , lies on .
As lies on , is the internal bisector of . As is also an altitude, this means that . By symmetry, and . Hence the triangle is equilateral.
Watch the video (Coming Soon)
Connected Program at Cheenta
Math Olympiad is the greatest and most challenging academic contest for school students. Brilliant school students from over 100 countries participate in it every year. Cheenta works with small groups of gifted students through an intense training program. It is a deeply personalized journey toward intellectual prowess and technical sophistication.