A circle is inscribed in ΔABC having sides 8 cm, 10 cm and 12 cm as s

1.	A circle is inscribed in ΔABC having sides 8 cm, 10 cm and 12 cm as shown in figure, Find AD, BE and CF.
Answer» We know that the tangents drawn from are external point to a circle are equal. Therefore AD = AF = x say. BD = BE = y say and CE = CF = z say Now, AB = 12 cm, BC = 8 cm, and CA= 10 cm. x + y = 12, y + z = 8 and z + x = 10 (x + y) + (y + z) + (z + x) = 12 + 8 + 10 2(x + y + z) = 30 x + y + z = 15 Now, x + y = 12 and x + y + z = 15 12 + z = 15 ⇒ z = 3 y + z = 8 and x + y + z = 15 x + 8 = 15 ⇒ x = 7 and z + x = 10 and x + y + z = 15 10 + y = 15 ⇒ y = 5 Hence, AD = x = 7 cm, BE = y = 5 cm and CF = z = 3 cm.

A circle is inscribed in ΔABC having sides 8 cm, 10 cm and 12 cm as shown in figure, Find AD, BE and CF.

Answer»

We know that the tangents drawn from are external point to a circle are equal.

Therefore AD = AF = x say.

BD = BE = y say and

CE = CF = z say

Now, AB = 12 cm, BC = 8 cm, and CA= 10 cm.

x + y = 12, y + z = 8 and z + x = 10

(x + y) + (y + z) + (z + x) = 12 + 8 + 10

2(x + y + z) = 30

x + y + z = 15

Now, x + y = 12 and x + y + z = 15

12 + z = 15 ⇒ z = 3

y + z = 8 and x + y + z = 15

x + 8 = 15 ⇒ x = 7

and z + x = 10 and x + y + z = 15

10 + y = 15 ⇒ y = 5

Hence, AD = x = 7 cm, BE = y = 5 cm and CF = z = 3 cm.