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ABCD is a parallelogram. L is a point on...

ABCD is a parallelogram. L is a point on BC which divides BC in the ratio `1:2`. AL intersects BD at P.M is a point on DC which divides DC in the ratio `1 : 2` and AM intersects BD in Q.
Point P divides AL in the ratio

A

`1:2`

B

`1:3`

C

`3:1`

D

`2:1`

Text Solution

Verified by Experts

The correct Answer is:
C

`BL=(1)/(3)b`
`thereforeAL=a+(1)/(3)b`
Let AP=`lamdaAL` and P divides DB in the ratio `mu:1-mu`
Then, `AP=lamda a+(lamda)/(3)b` . . . (i)
Also, `AP=mua+(1-mu)b` . . (ii)
From eqs. (i) and (ii),
`lamda a+(lamda)/(3)b=mua+(1-mu)b`
`therefore lamda=mu`
and `(lamda)/(3)=1-mu`
`therefore lamda=(3)/(4)`
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