Q. 25.0( 1 Vote )

In m ABCD, T and intersects in M and in O. Prove that AM2 = MT • MO.

Answer :

In ABCD, T and intersects in M and in O.

To prove:

AM2 = MT •MO

In ∆AMB and ∆OMD

AMD OMD (Vertically opposite angles)

MBA MDO (Alternate angles)

The correspondence AMDOMB is a similarity


In ∆AMD and ∆TMB

AMD TMB (Vertically opposite angles)

MAD MTB (Alternate angles)

The correspondence AMDTMB is a similarity


Multiplying (1) and (2),

Hence, AM2 = MT •MO

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