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Question
Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half the hypotenuse.
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Solution
We have to prove that ` BP = 1/2 AC`
Let Δ ABC be a right angle at B and P be midpoint of AC
Draw a circle with center at P and AC diameter
Since ` angle ABC = ` 90° therefore circle passing through B
So `BP = CP = `radius
`⇒ AP = BP = CP `
Hence
`BP = 1/2 AC` Proved.
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