A circle is inscribed in a ΔABC having sides AB = 16 cm, BC = 20 cm and AC = 24 cm, and side AB, BC and AC touches circle at D, E and F, respectively. The measure of AD is:
Answer & explanation
Correct answer: option 1
As from point A two tangent is drawn on the circle
⇒ AD = AF = a
Similarly, from point B two tangent is drawn on the circle
⇒ BD = BE = b
Similarly, from point C two tangent is drawn on the circle
⇒ CE = CF = c
According to the question
⇒ AB = a + b
⇒ 16 = a + b ..(1)
⇒ BC = b + c
⇒ 20 = b + c ..(2)
⇒ AC = a+ c
⇒ 24 = a + c ..(3)
Now, on adding eq (1), (2) and (3), we get
⇒ 16 + 20 + 24 = a + b + b + c + a + c
⇒ a + b + c = 30
Now put the value of b + c in above equation, we get
⇒ a + 20 = 30
⇒ a = 10 cm
Therefore, the value of AD is 10 cm.