MathDB

10

Part of 1969 IMO Shortlist

Problems(1)

Identity between Brocard angle and median angle

Source:

9/29/2010
(BUL4)(BUL 4) Let MM be the point inside the right-angled triangle ABC(∠C=90∘)ABC (\angle C = 90^{\circ}) such that ∠MAB=∠MBC=∠MCA=ϕ.\angle MAB = \angle MBC = \angle MCA =\phi. Let Ψ\Psi be the acute angle between the medians of ACAC and BC.BC. Prove that sin⁡(ϕ+Ψ)sin⁡(ϕ−Ψ)=5.\frac{\sin(\phi+\Psi)}{\sin(\phi-\Psi)}= 5.
trigonometrygeometryIMO LonglistIMO ShortlistTrigonometric Equationsmedian