Question

# In the given figure DA⊥AB,CB⊥AB and OM⊥AB. If AO = 5.4 cm, OC = 7.2 cm and BO = 6 cm, then the length of DO is:

A
4.5 cm
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B
4 cm
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C
5 cm
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D
6.5 cm
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Solution

## The correct option is B 4.5 cmConsider ΔCABandΔOAM.∠OMA=∠CBA=∠900∠OAM=∠CAB[commonangle]∠AOM=∠ACB[correspondingangles] [two lines perpendicular to the base are parallel to one another]Hence ΔOAM∼ΔCAM by AAA.So, AOAC=AMAB=5.412.6Similarly, consider ΔDBAandΔOBM.∠OMB=∠DAB=∠900∠OBM=∠DBA[commonangle]∠BOM=∠BDA[correspondingangles] [two lines perpendicular to the base are parallel to one another]Hence ΔOBM∼ΔDBA by AAA.So, AOAC=AMAB=5.412.6andBOBD=BMAB=AB−AMAB=1−AMAB=1−5.4.12.6BOBD=7.212.6⟹6BD=7.212.6⟹BD=10.5IfBD=10.5andOB=6thenDO=4.5.

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