M is the mid point of side AB of equilateral triangle ABC. P is a point on BC such that AP + PM is minimum. If AB = 20 then AP + PM is

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Solution

The correct option is A
Take the reflection of $△ A B C$ in BC.

PM = PM'
PA + PM = PA + PM' it is minimum when M' PA lies in a line
Now apply cosine rule in triangle ABM'
We will get AM' = $10 \sqrt{7}$

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M is the mid point of side AB of equilateral triangle ABC. P is a point on BC such that AP + PM is minimum. If AB = 20 then AP + PM is

The correct option is A Take the reflection of △ABC in BC. PM = PM' PA + PM = PA + PM' it is minimum when M' PA lies in a line Now apply cosine rule in triangle ABM' We will get AM' = 10√7

The correct option is A
Take the reflection of $△ A B C$ in BC.

PM = PM'
PA + PM = PA + PM' it is minimum when M' PA lies in a line
Now apply cosine rule in triangle ABM'
We will get AM' = $10 \sqrt{7}$