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Question

PR and PQ are tangents from P to the center with centre O. If BC is tangent to the circle at X. Prove that PC+CX=PB+BX.
1140279_d5aab28746e34b47bf578932563895e0.png

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Solution

R.E.F image
PR=PQ
So, PC+CR
PB+BQ....(1)

As tangent from extant point of circle are equal
So, : CX=CR
and xb=bq....(2)
So PC+CR=PB+BQ (from (1))
PC+CX=PB+XB (from (2))
Hence proved
eqn of circle : x2+y26x10y+λ
radius of circle (g,f)(3,5)
radius circle 73
λ752,λ725


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