CircleMedium

Question

3 circle of radii 1, 2 and 3 and centres at A, B and C respectively, touch each other. An other circle whose centre is P touches all these 3 circles externally and has radius r. Also ∠PAB = θ & ∠PAC = α -

Options

A.cosθ =
B.cos α =
C.r =
D.r =

Solution

  
ᐃABC is right angle
Applying cosine rule in ᐃPAB
cos θ =
=
Again applying cosine rule in ᐃPAC
cos α =
∵  α + θ = 90o
α = 90o - θ        cos α = sin θ
=

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