MathDB

1

Part of 1989 National High School Mathematics League

Problems(2)

Complex Plane

Source: 1989 National High School Mathematics League, Exam One, Problem 1

2/25/2020
On complex plane, if A,BA,B are two angles of acute triangle ABCABC, then the point z=(cos⁡B−sin⁡A)+i(sin⁡B−cos⁡A)z=(\cos B-\sin A)+\text{i}(\sin B-\cos A) corresponding to is in (A)\text{(A)}Quadrant I (B)\text{(B)}Quadrant II (C)\text{(C)}Quadrant III (D)\text{(D)}Quadrant IV
Geometry Problem

Source: 1989 National High School Mathematics League, Exam Two, Problem 1

2/25/2020
In △ABC\triangle ABC, AB>ACAB>AC, bisector of outer angle ∠A\angle A intersects circumcircle of △ABC\triangle ABC at EE. Projection of EE on ABAB is FF. Prove that 2AF=AB−AC2AF=AB-AC.
geometry