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C is a point outside circle with centre A. and radius "r". CB and CD are tangents segments whose length is "t". find area of triangle BCD in terms of "r" and "t"

C is a point outside circle with centre A. and radius "r".


CB and CD  are tangents segments whose length is "t".


find area of triangle BCD in terms of "r" and "t"

Grade:10

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear ajinka


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CA = √r2+t2

sinθ =r/√r2+t2

cosθ = t/√r2+t2

AP =rsinθ  = r2/√r2+t2

BP =rcosθ = tr/√r2+t2

ΔBCD = =2ΔBCP = 2[ΔABC -ΔABP]

                        =2[rt/2   - 1/2 AB * BP]

                        =rt - {r2/√r2+t2}{ tr/√r2+t2}

                        =rt - r3t/(r2+t2)

                        =rt3/(r2+t2)

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Badiuddin


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