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Omni-MATH / Triangle ABC has AB=10,BC=17, and CA=21. Point P lies on the circle with diameter AB. What is the greatest possible area of APC?

Problem

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problem

Triangle ABCA B C has AB=10,BC=17A B=10, B C=17, and CA=21C A=21. Point PP lies on the circle with diameter ABA B. What is the greatest possible area of APCA P C?
Plain-text mathematical notation (without MathML)
Triangle ABC has AB=10,BC=17, and CA=21. Point P lies on the circle with diameter AB. What is the greatest possible area of APC?
Original LaTeX notation
Triangle $A B C$ has $A B=10, B C=17$, and $C A=21$. Point $P$ lies on the circle with diameter $A B$. What is the greatest possible area of $A P C$?

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Source and history

task_id
737a6858-40fd-52c9-9ac7-ff3cb3e7a9d7
task_key
test--737a6858-40fd-52c9-9ac7-ff3cb3e7a9d7
task_revision_id
1
config / split
/ test

Official source

initial import