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In right triangle ABC, right angle is at...

In right triangle ABC, right angle is at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see figure). Show that :
`(i) DeltaAMC ~= DeltaBMD`
`(ii) /_DBC` is a right angle
`(iii) Delta DBC ~= DeltaACB` (iv)`CM = 1/2 AB`.

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