In triangle $ABC,$ altitudes $\overline{AD}$

  1. Altitudes $\overline{XD}$ and $\overline{YE}$ of acute triangle $\triangle XYZ$ intersect at point $H$. If the altitudes
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  2. Altitudes $\overline{XD}$ and $\overline{YE}$ of acute triangle $\triangle XYZ$ intersect at point $H$. If the altitudes
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  3. Altitudes $\overline{XD}$ and $\overline{YE}$ of acute triangle $\triangle XYZ$ intersect at point $H$. If the altitudes
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  4. Altitudes $\overline{XD}$ and $\overline{YE}$ of acute triangle $\triangle XYZ$ intersect at point $H$. If the altitudes
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  5. Altitudes $\overline{XD}$ and $\overline{YE}$ of acute triangle $\triangle XYZ$ intersect at point $H$. If the altitudes
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  6. Altitudes $\overline{XD}$ and $\overline{YE}$ of acute triangle $\triangle XYZ$ intersect at point $H$. If the altitudes
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  7. In triangle $XYZ,$ $M$ is the midpoint of $\overline{XY}.$ Let $D$ be the point on $\overline{YZ}$ such that $\overline{XD}$
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  8. In triangle ABO, M is the midpoint of \overline{AB}. Points C, D, and N lie on line segments $\overline{AO},$ $\overline{BO},$
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  9. Let the incircle of triangle $ABC$ be tangent to sides $\overline{BC}$, $\overline{AC}$, and $\overline{AB}$ at $D$, $E$, and
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  10. In acute triangle $ABC$, points $D$, $E$, and $F$ are located on sides $\overline{BC}$, $\overline{AC}$, and $\overline{AB}$ so
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