A triangle ABC is drawn to circumscribe a circle of radius 3cm such that the segments BD and DC are respectively of lengths 6cm and 9cm . If the area of triangle ABC is 54cm^2 then find the lengths of AB and AC
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Answer:
Missing information :
Area of triangle = 54 cm²
Let say AB touches circle at Q & AC at R
BQ = BD = 6 cm ( equal tangent)
CR = CD = 9 cm ( equal tangent)
AQ = AR = x
Area of triangle = (1/2) * r ( AB + AC + BC)
= (1/2) * 3 ( 6 + x + 9 + x + 6 + 9)
= (1/2) * 3(30 + 2x)
= 3 ( 15 + x)
3 ( 15 + x) = 54
=> 15 + x = 18
=> x = 3
AB = 9
AC = 12
Step-by-step explanation:
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