Question Number 212986 by MrGaster last updated on 27/Oct/24
Commented by MrGaster last updated on 27/Oct/24
A, B are two fixed points on the same side of the line PQ. M is a moving point on PQ. When (|AM|+|BM|) is minimized, prove: angle AMP = angle BMQ
Answered by mr W last updated on 29/Oct/24
Commented by mr W last updated on 29/Oct/24
$${BM}={B}'{M} \\ $$$${AM}+{BM}={AM}+{B}'{M},\:{which}\:{is} \\ $$$${minimal}\:{when}\:{A},{M},{B}'\:{are}\:{on}\:{the} \\ $$$${same}\:{straight}.\:{in}\:{this}\:{case}\:\alpha=\beta. \\ $$