Question

A circle is inscribed in a triangle ABC touching the side AB at D such that AD = 5, BD = 3. If ŠA = 60⁰ then length BC

Equals

• A. 9
• B. $\frac { 120 } { 13 }$
• C. 13
• D. 12

Answer 1

Answer: (C)

13

Answer 2

Q tan 30⁰ = $\frac { \mathrm { r } } { 5 }$

Ž r =$\frac { 5 } { \sqrt { 3 } }$

Now tan ……..(i)

Now cos B

\ sin B $= \frac { \sqrt { 675 } } { 26 } = \frac { 15 \sqrt { 3 } } { 26 }$

\ sin C = sin(A + B) = sinA cosB + cosAsinB

= $\frac { 4 \sqrt { 3 } } { 13 }$

Now a = 13