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Omni-MATH / Triangle ABC obeys AB=2AC and ∠BAC=120^(∘). Points P and Q lie on segment BC such that begin{aligned} AB^{2}+BC cdot CP & =BC^{2} 3AC^{2}+2BC cdot CQ & =BC^{2} end{aligned} Find …

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problem

Triangle ABCABC obeys AB=2ACAB=2AC and ∠BAC=120∘\angle BAC=120^{\circ}. Points PP and QQ lie on segment BCBC such that $$\begin{aligned} AB^{2}+BC \cdot CP & =BC^{2} \\ 3AC^{2}+2BC \cdot CQ & =BC^{2} \end{aligned}$$ Find ∠PAQ\angle PAQ in degrees.
Plain-text mathematical notation (without MathML)
Triangle ABC obeys AB=2AC and ∠BAC=120^(∘). Points P and Q lie on segment BC such that $$\begin{aligned} AB^{2}+BC \cdot CP & =BC^{2} \\ 3AC^{2}+2BC \cdot CQ & =BC^{2} \end{aligned}$$ Find ∠PAQ in degrees.
Original LaTeX notation
Triangle $ABC$ obeys $AB=2AC$ and $\angle BAC=120^{\circ}$. Points $P$ and $Q$ lie on segment $BC$ such that $$\begin{aligned} AB^{2}+BC \cdot CP & =BC^{2} \\ 3AC^{2}+2BC \cdot CQ & =BC^{2} \end{aligned}$$ Find $\angle PAQ$ in degrees.

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Source and history

task_id
213f0043-3e5d-54e9-b80c-6a6f13693ebf
task_key
test--213f0043-3e5d-54e9-b80c-6a6f13693ebf
task_revision_id
1
config / split
/ test

Official source

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