MathDB

3

Part of 2019 South Africa National Olympiad

Problems(1)

SAMO Problem 3: Product of lengths in triangle with $45^\circ$ angle

Source: South African Mathematics Olympiad 2019, Problem 3

7/25/2019
Let AA, BB, CC be points on a circle whose centre is OO and whose radius is 11, such that ∠BAC=45∘\angle BAC = 45^\circ. Lines ACAC and BOBO (possibly extended) intersect at DD, and lines ABAB and COCO (possibly extended) intersect at EE. Prove that BD⋅CE=2BD \cdot CE = 2.
geometry