a triangle ABC is drawn to circumscribe a circle of radius 3 cm, such that the segments BD and DC - Maths - Areas Related to Circles

Question

a triangle ABC is drawn to circumscribe a circle of radius 3 cm,
such that the segments BD and DC into BC is divided by the point of
contact D are the lenghs 6 cm and 8 cm resp Find the side AB if the
area of triangle = 63 sq cms

Priyanka Kedia · Accepted Answer

Given, a triangle ABC is drawn to circumscribe a circle of radius 3 cm. So, OD = OM = ON = 3 cm

length BD = 6 cm and length CD = 8 cm

We know that, length of two tangents drawn from an external point of circle are equal. Therefore,

$B D = B M = 6 c m C D = C N = 8 c m L e t A M = x c m, S o, A M = A N = x c m T h u s, A B = (x + 6) c m B C = (6 + 8) c m = 14 c m a n d C A = (8 + x) c m N o w, I n Δ A B C, a r (Δ A B C) = a r (Δ O A B) + a r (Δ O B C) + a r (Δ O C A) G i v e n, a r (Δ A B C) = 63 {c m}^{2}, T h e r e f o r e, \Rightarrow 63 = (\frac{1}{2} \times O M \times A B) + (\frac{1}{2} \times O D \times B C) + (\frac{1}{2} \times O N \times C A) \Rightarrow 63 = (\frac{1}{2} \times 3 \times (6 + x)) + (\frac{1}{2} \times 3 \times 14) + (\frac{1}{2} \times 3 \times (8 + x)) \Rightarrow 63 = \frac{1}{2} (18 + 3 x + 42 + 24 + 3 x) \Rightarrow 63 \times 2 = 6 x + 84 \Rightarrow 126 = 6 x + 84 \Rightarrow 42 = 6 x \Rightarrow x = 7 c m H e n c e, t h e s i d e A B = (6 + x) c m = (6 + 7) c m = 13 c m$

a triangle ABC is drawn to circumscribe a circle of radius 3 cm, such that the segments BD and DC into BC is divided by the point of contact D are the lenghs 6 cm and 8 cm resp. Find the side AB if the area of triangle = 63 sq.cms