Question

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.

Answer 1

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)]`