In Fig. 3, a circle inscribed in triangle ABC touches its sides AB, BC, and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.

Fig.3

Question

In Fig. 3, a circle inscribed in triangle ABC touches its sides AB, BC, and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF. Fig.3

Philoid · Accepted Answer

In the fig.3,

AD and AF are making a pair of tangents drawn from vertex A of Δ ABC on the circle.

∴ AD = AF = x [LET]

[∵ Tangents drawn from an exterior point to the circle are equal in length]

BD and BE are making a pair of tangents drawn from vertex B of Δ ABC on the circle.

∴ BD = BE = y [LET]

[∵ Tangents drawn from an exterior point to the circle are equal in length]

CE and CF are making a pair of tangents drawn from vertex C of Δ ABC on the circle.

∴ CE = CF = z [LET]

[∵ Tangents drawn from an exterior point to the circle are equal in length]

From fig.3-

AF+CF = x+z = 10 cm …(1)

BE+CE = y+z = 8 cm …(2)

AD+BD = x+y = 12 cm …(3)

Adding equations (1), (2) and (3), we get-

2(x+y+z) = 30

⇒ x+y+z = 15 …(4)

Subtracting equations (1), (2) and (3) from (4) one bye one, we get-

x = 7 cm, y = 5 cm, z = 3 cm

Thus, Length of AD = 7 cm

Length of BE = 5 cm

and, Length of CF = 3 cm.

In Fig. 3, a circle inscribed in triangle ABC touches its sides AB, BC, and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.Fig.3

In Fig. 3, a circle inscribed in triangle ABC touches its sides AB, BC, and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.

Fig.3