Omni-MATH / Let ABC be an acute scalene triangle and let P be a point in its interior. Let A₁, B₁, C₁ be projections of P onto triangle sides BC, CA, AB, respectively. Find the locus of points…

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Let ABC be an acute scalene triangle and let P be a point in its interior. Let A₁, B₁, C₁ be projections of P onto triangle sides BC, CA, AB, respectively. Find the locus of points P such that AA₁, BB₁, CC₁ are concurrent and ∠PAB+∠PBC+∠PCA=90^(∘).

Let $ABC$ be an acute scalene triangle and let $P$ be a point in its interior. Let $A_1$, $B_1$, $C_1$ be projections of $P$ onto triangle sides $BC$, $CA$, $AB$, respectively. Find the locus of points $P$ such that $AA_1$, $BB_1$, $CC_1$ are concurrent and $\angle PAB + \angle PBC + \angle PCA = 90^{\circ}$.

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task_id

525d3364-4c27-5795-add8-57a11f29fd2e

task_key

test--525d3364-4c27-5795-add8-57a11f29fd2e

task_revision_id

3

config / split

/ test

Official source

initial import