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In Fig. 6.44, ABC and DBC are two triang...

In Fig. 6.44, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that `(ar (ABC))/( ar (DBC))`= `(AO )/( DO )`

Text Solution

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Consider `/_AOM` and`/_DNO`
`/_AOM=/_DON`(oppesite angles)
`/_AMO=/_DNO=90^@`
`/_AOM cong /_DNO`
`(ar(/_AOM))/(ar(/_DNO))=(AM)^2/(DN)^2=(AO)^2/(DO)^2`
Ratio of the area of similar triangles is equal too the square of their corresponding sides.
`(AM)^2/(DN)^2=(AO)^2/(DO)^2`
`(AM)/(DN)=(AO)/(DO)-(1)`
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