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ABC is a triangle right-angled at C. A l...

ABC is a triangle right-angled at C. A line through the midpoint P of hypotenuse AB and parallel to BC intersects AC at M. Show that
`"(i) "` M is the midpoint of `AC,`
` "(ii) " MP bot AC ,`
` "(iii) " CP = AP=(1)/(2)AB. `

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