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

Answer 1

Given: PA and PB are the tangents to the circle. 
PA = 12 cm
QC = QD = 3 cm    

To find: PC + PD

PA = PB = 12 cm                (The lengths of tangents drawn from an external point to a circle are equal)
Similarly, QC = AC = 3 cm 
and QD = BD = 3 cm.

Now, PC = PA − AC = 12 − 3 = 9 cm
Similarly, PD = PB − BD = 12 − 3 = 9 cm

Hence, PC + PD = 9 + 9 = 18 cm.