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:

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 07 Dec 2022 Shift 2)

Answer 1

Given:

A circle is inscribed in a ΔABC having sides AB = 16 cm, BC = 20 cm and AC = 24 cm

Side AB, BC and AC touch circle at D, E and F

Concept used:

When two tangent is drawn from same point on the circle then the length of the both of the chord will be same

Calculation:

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

⇒ 60 = 2(a + b + c)

⇒ a + b + c = 30

Now put the value of b + c in above equation, we get

⇒ a + 20 = 30

⇒ a = 10 cm

⇒ Hence, The value of AD is 10 cm