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Omni-MATH / Let Γ denote the circumcircle of triangle ABC. Point D is on (AB)¯ such that (CD)¯ bisects ∠ACB. Points P and Q are on Γ such that (PQ)¯ passes through D and is perpendicular to …

Problem

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problem

Let Γ\Gamma denote the circumcircle of triangle ABCA B C. Point DD is on AB¯\overline{A B} such that CD¯\overline{C D} bisects ∠ACB\angle A C B. Points PP and QQ are on Γ\Gamma such that PQ¯\overline{P Q} passes through DD and is perpendicular to CD¯\overline{C D}. Compute PQP Q, given that BC=20,CA=80,AB=65B C=20, C A=80, A B=65.
Plain-text mathematical notation (without MathML)
Let Γ denote the circumcircle of triangle ABC. Point D is on (AB)¯ such that (CD)¯ bisects ∠ACB. Points P and Q are on Γ such that (PQ)¯ passes through D and is perpendicular to (CD)¯. Compute PQ, given that BC=20,CA=80,AB=65.
Original LaTeX notation
Let $\Gamma$ denote the circumcircle of triangle $A B C$. Point $D$ is on $\overline{A B}$ such that $\overline{C D}$ bisects $\angle A C B$. Points $P$ and $Q$ are on $\Gamma$ such that $\overline{P Q}$ passes through $D$ and is perpendicular to $\overline{C D}$. Compute $P Q$, given that $B C=20, C A=80, A B=65$.

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Source and history

task_id
63453622-a21a-5c2f-8edd-3866bf33ad7d
task_key
test--63453622-a21a-5c2f-8edd-3866bf33ad7d
task_revision_id
1
config / split
/ test

Official source

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