MathDB

17

Part of 2023 Assam Mathematics Olympiad

Problems(1)

Assam Mathematics Olympiad 2023 Category III Q17

Source:

9/11/2024
If in △ABC\bigtriangleup ABC, ADAD is the altitude and AEAE is the diameter of the circumcircle through AA, then prove that AB⋅AC=AD⋅AEAB\cdot AC = AD \cdot AE. Use this result to show that if ABCDABCD is a cyclic quadrilateral then show that AC⋅(AB⋅BC+CD⋅DA)=BD⋅(DA⋅AB+BC⋅CD)AC \cdot (AB \cdot BC + CD \cdot DA) = BD\cdot (DA\cdot AB + BC \cdot CD).
geometrycircumcircle