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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
147 Points
11 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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Regards,
Askiitians Experts
Badiuddin


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