Talk:2021 AIME I Problems/Problem 9
Based on Solution 1:
Note: Instead of solving the system of equations (1)(2) which can be time consuming, by noting that by AA, we could find out , which gives . We also know that by Pythagorean Theorem on . . Then using Pythagorean Theorem on we obtain: substituting, we get: Finally, we solve to obtain .
~Chupdogs
However, I don't think is convincing. How do you find that by AA?
One right angle is shared and by alternate angles theorem (for first part) and symmetry for the second part as its an isosceles trapezoid ( and are both diagonals and the angles it makes with the base edge is the same)