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Omni-MATH / Points D,E,F lie on circle O such that the line tangent to O at D intersects ray (EF)→ at P. Given that PD=4,PF=2, and ∠FPD=60^(∘), determine the area of circle O.

Problem

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problem

Points D,E,FD, E, F lie on circle OO such that the line tangent to OO at DD intersects ray EF→\overrightarrow{E F} at PP. Given that PD=4,PF=2P D=4, P F=2, and ∠FPD=60∘\angle F P D=60^{\circ}, determine the area of circle OO.
Plain-text mathematical notation (without MathML)
Points D,E,F lie on circle O such that the line tangent to O at D intersects ray (EF)→ at P. Given that PD=4,PF=2, and ∠FPD=60^(∘), determine the area of circle O.
Original LaTeX notation
Points $D, E, F$ lie on circle $O$ such that the line tangent to $O$ at $D$ intersects ray $\overrightarrow{E F}$ at $P$. Given that $P D=4, P F=2$, and $\angle F P D=60^{\circ}$, determine the area of circle $O$.

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Source and history

task_id
b5743634-bd9f-5b95-a1fc-f088017cdcc4
task_key
test--b5743634-bd9f-5b95-a1fc-f088017cdcc4
task_revision_id
1
config / split
/ test

Official source

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