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Lengths of Tangents Drawn from External Point

In figure, PA...

Question

In 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 = QD = 3 cm, then find PC + PD.

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Solution

PA=PB=12 cm (length of tangent)

Similarly,
QC=AC=3 cm
QD=BD=3cm
PC=PA-AC=12-3=9cm
Similarly
PD=PB-BD=12-3=9cm
Hence,
PC+PD=9+9=18cm

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