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In the given figure, PA and PB are tange...

In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA =12 cm, QC=3cm, then find PC+PD.

Text Solution

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Since, the length of the two tangents drawn from an external point to a circle are equal therefore,
`PA=PB" "…(1)`
`CA=CQ" "…(2)`
and `" "DB=DQ" "…(3)`
Now,
`PA=12" "`(given)
`PC+CA=12`
`implies" "PC+CQ=12" "`[From (2)]
`implies" "PC+3=12" "implies" "PC=9cm" "...(4)`
Also `PB=PA=12" "`[From(1)]
`implies" "PD+DB=12`
`implies" "PD+DQ=12" "`[From (3)]
`implies" "PD+3=12`
`PD=9cm" "...(5)]`
`:." "PC+PD=(9+9)cm=18cm" "[From (4) and (5)]`
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