Question 24
In trapezium $ABCD$, $AB\parallel CD$, $AB=36$, $BC=15$, and $DA=12$. Point $P$ lies on $AB$, and a circle centred at $P$ is tangent to both $BC$ and $AD$. Evaluate $AP^2+BP^2$.
Use only the two stated tangencies to BC and AD. The original sketch supplies no additional tangency condition to CD.
Original source figure (not to scale), with its printed mathematical labels preserved.
Use only the two stated tangencies to BC and AD. The original sketch supplies no additional tangency condition to CD.
Original source figure (not to scale), with its printed mathematical labels preserved.