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Omni-MATH / Let ABC be a triangle with AB=6,AC=7,BC=8. Let I be the incenter of ABC. Points Z and Y lie on the interior of segments AB and AC respectively such that YZ is tangent to the incirc…

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problem

Let ABCA B C be a triangle with AB=6,AC=7,BC=8A B=6, A C=7, B C=8. Let II be the incenter of ABCA B C. Points ZZ and YY lie on the interior of segments ABA B and ACA C respectively such that YZY Z is tangent to the incircle. Given point PP such that ∠ZPC=∠YPB=90∘\angle Z P C=\angle Y P B=90^{\circ} find the length of IPI P.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=6,AC=7,BC=8. Let I be the incenter of ABC. Points Z and Y lie on the interior of segments AB and AC respectively such that YZ is tangent to the incircle. Given point P such that ∠ZPC=∠YPB=90^(∘) find the length of IP.
Original LaTeX notation
Let $A B C$ be a triangle with $A B=6, A C=7, B C=8$. Let $I$ be the incenter of $A B C$. Points $Z$ and $Y$ lie on the interior of segments $A B$ and $A C$ respectively such that $Y Z$ is tangent to the incircle. Given point $P$ such that $$\angle Z P C=\angle Y P B=90^{\circ}$$ find the length of $I P$.

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Source and history

task_id
12190e12-b063-55a7-8266-08181ce1eea3
task_key
test--12190e12-b063-55a7-8266-08181ce1eea3
task_revision_id
1
config / split
/ test

Official source

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