Question

6. In Figure 4, a triangle ABC is drawn to circumscribe a circle of radius 3 cm, such that the
segments BD and DC are respectively of lengths 6 cm and 9 cm. If the area of triangle ABC is 54 cm square, then find the lengths of sides AB and AC.
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Answer 1

Answer:

change the radius and the length

Answer 2

Answer:

Step-by-step explanation:

We know that tangent segments to a circle from the same external point are congruent.

Now, we have

AE = AF, BD = BE = 6 cm and CD = CF = 9 cm

Now,

Area△ABC=Area△BOC+Area△AOB+Area△AOC⇒54=12×BC×OD+12×AB×OE+12×AC×OF⇒108=15×3+6+x×3+9+x×3⇒36=15+6+x+9+x

⇒36=30+2x⇒2x=6⇒x=3 cm

∴ AB = 6 + 3 = 9cm and AC = 9 + 3 = 12 cm