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


…(1)


In ∆AMD and ∆TMB


AMD TMB (Vertically opposite angles)


MAD MTB (Alternate angles)


The correspondence AMDTMB is a similarity


…(2)


Multiplying (1) and (2),




Hence, AM2 = MT •MO


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