##### Ritesh

#### Question

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**Question**

18-09-05

**Answer**

ABCD is a rhombus. A Straight line through C cuts AD produced at P and AB produced at Q. If DP=(1/2)AB, then the ratio of the length of BQ and AB is

**Solution**

AB=2DP

In triangle QBC and triangle QAP

Angle QCB=Angle QPA (corresponding angle)

Angle QBC= Angle QAP (corresponding angle)

Triangle QBC similar to triangle QAP

Therefore BQ/AQ=BC/AP

BQ/(AB+BQ)=BC/(AD+DP)

BQ/(AB+BQ)=BC/(AB+1/2AB) ( AD=AB=BC=CD and AB=2DP)

BQ/(AB+BQ)=BC/(3/2*AB)

BQ/(AB+BQ)=2/3 ( AB CANCELLED BC as both are equal)

3 BQ=2AB+2BQ

BQ=2AB

BQ/AB=2/1