As shown in the figure, it is known that point a is a point in the acute angle ∠ mon. Try to determine point B and point C on OM and on respectively to minimize the perimeter of △ ABC As shown in the figure, it is known that point a is a point in the acute angle ∠ mon. Try to determine point B and point C on OM and on respectively to minimize the perimeter of △ ABC, and explain the reason

Let a be the symmetric point A1 of on, and let a be the symmetric point A2 of OM,
The minimum perimeter of △ ABC is obtained by connecting a 1 a 2, intersecting om with B and intersecting on with C
Reason: A and A1 are symmetrical about on, so AC = A1C, similarly, ab = A2B
So AB + BC + Ca = A1A2
So AB + BC + Ca is the shortest
That is, the perimeter of △ ABC is the smallest

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