O is the centre of the circle. AP, PC And CD are the tangents. If AP=4cm and CD=5cm then the length of PC is ?
Answers
If AP = 4cm and CD = 5cm then the length of PC is 9 cm.
Step-by-step explanation:
It is given that,
O is the centre of the circle
AP, PC & CD are the tangents to the circle
AP = 4 cm
CD = 5 cm
Let tangent PC touch the circle at A, R & D as shown in the figure attached below.
We know that according to the Two-Tangent theorem, if two tangents are drawn to one circle from the same external point, then they are congruent to each other.
∴ AP = RP = 4 cm ….. (i)
And,
CD = RC = 5 cm ….. (ii)
From the figure, we get
PC = RP + RC
Substituting from (i) & (ii), we get
⇒ PC = 4 + 5
⇒ PC = 9 cm
Thus, the length of PC is 9 cm.
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Step-by-step explanation:
AP=PR (tangent from external point)
CD=CR(tangent from external point)
AP=4 CD=5 PR+CR=PC
4+5=9