Question

C, and C2 are two circles touching each
otherexternally at B. CA and CB are tangents
from apoint Con C1. If PC = 16 cm and PD = 9, then the length of CA is.​

Answer 1

Answer:

Sorry I can't understand.

Sorry

Answer 2

Consider, ΔBC1​E and ΔBC2​F

⇒∠E=∠F=90∘

⇒C1​E∥C2​F

That means implies they are similar.

BC2​BC1​​=BFBE​

⇒r1​/r1+r1​+r2​r​​=1/3+1/2   .....(∵centre C1​,C2​bisect BA1​,A2​A3​with ⊥at E,F)

⇒3r1​=2r2​

⇒r2​=3/2​r1​

Also if P is an external point from which a secant cutting the circle at A,B, then PA×PB=costant

Thus BC1​×BC2​=BE×BF

⇒4r1​(r1​+r2​)=4×3

⇒r1 square ​+3/2​r1 square ​=4

⇒r1 square ​= 6/5

⇒r1​= √30/5

​​

And r2​= 3/2 x √30/5

​​= 3√3/10.

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