Problem

Problem of the Day #19

POTD December 8, 2023
Author: qgek

In the unit cube $ABCD- A_1B_1C_1D_1,$ point P is the midpoint of $CC_1$ , and point $Q$ is the midpoint of $A_1B_1$ . Point $M$ lies on segment $AD$ , and $AM : MD = 2 : 1$ . The plane $MQP$ intersects $B_1C_1$ at point H. If the area of $\triangle BHP = \frac{m}{n}$ , where $m$ and $n$ are positive coprime integers, find $m + n$ .

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Category: Problem of the Day
Points: 4
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