MathDB

In an acute triangle

ABC

, let

\overline {AK}, \overline {BL}, \overline {CM}

be the altitudes of the triangle concurrent at the point

H

and let

P

the midpoint of

\overline {AH}

. Let's define

S = \overline {BH} \cap \overline {MK}

and

T = \overline {LP} \cap \overline {AB}

. Show that

\overline {TS} \perp \overline {BC}

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