Question

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

Answer 1

AB = 9 cm & AC = 12 cm

Step-by-step explanation:

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

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Answer 2

Answer:

AB= 9 and AC = 12

hope this is useful