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Omni-MATH / Triangle ABC has AB=1,BC=√(7), and CA=√(3). Let ℓ₁ be the line through A perpendicular to AB,ℓ₂ the line through B perpendicular to AC, and P the point of intersection of ℓ₁ and ℓ₂…

Problem

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problem

Triangle ABCA B C has AB=1,BC=7A B=1, B C=\sqrt{7}, and CA=3C A=\sqrt{3}. Let ℓ1\ell_{1} be the line through AA perpendicular to AB,ℓ2A B, \ell_{2} the line through BB perpendicular to ACA C, and PP the point of intersection of ℓ1\ell_{1} and ℓ2\ell_{2}. Find PCP C.
Plain-text mathematical notation (without MathML)
Triangle ABC has AB=1,BC=√(7), and CA=√(3). Let ℓ₁ be the line through A perpendicular to AB,ℓ₂ the line through B perpendicular to AC, and P the point of intersection of ℓ₁ and ℓ₂. Find PC.
Original LaTeX notation
Triangle $A B C$ has $A B=1, B C=\sqrt{7}$, and $C A=\sqrt{3}$. Let $\ell_{1}$ be the line through $A$ perpendicular to $A B, \ell_{2}$ the line through $B$ perpendicular to $A C$, and $P$ the point of intersection of $\ell_{1}$ and $\ell_{2}$. Find $P C$.

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Source and history

task_id
2f70ea4f-6830-5084-84d6-01b5ca52fa23
task_key
test--2f70ea4f-6830-5084-84d6-01b5ca52fa23
task_revision_id
1
config / split
/ test

Official source

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