1.

Two circles with unequal radii,centred at A and B respectively,touch each other externally at T.If BD is tangent to the first circle at D and TC is transverse common tangent meeting BD at C.Also,AT has the length 3 and BT has length 2. Then the length of CD is equal to

Answer»

2
`5/2`
`3/2`
`1/2`

SOLUTION :
BT=2 , AT=3=AD
`therefore` AB=5 , AD=3
`therefore` BD=4
From triangle BTC: `COSTHETA="BT"/"BC"=2/"BC"`….(1)
From triangle BAD : `cos theta="BD"/"BA"`
`costheta=4/5` ….(2)
From (1) and (2)
`2/"BC"=4/5 rArr BC=5/2`
`therefore` CD=BD-BC
`=4-5/2`
`=3/2`


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