दी गयी आकृति में, त्रिभुज ABC

1.	दी गयी आकृति में, त्रिभुज ABC का अंत: केंद्र 0 है। यदिAO 5 Om CO 32 -7 = = तथा 6 = , है, तो BO/OF का मान क्या है ?ABEC
Answer» Solution Construction: Draw : AE ⊥ BC Draw; BF ⊥ AC Draw : DC ⊥ AB O is the intersection point . Given That: AO /OE = 5/4 and OC /OD = 3/2 Let BC = a, CA = b, and AB = c ∴AO/OE = b+c/a = OC/OD = b+c/c ∴ b+c/a = 5/4 ⇒b+c+a/a = 5+4/4 = 9/4 -----(1) and b+a/ c = 3/2 ∴ a+b+c/c = 3+2/2 = 5/2 --(2) on Dividing eq. (2) by (1) we get. a/c = 5/2 Χ 4/9 = 10/9 ⇒ a = 10k and c = 9k ⇒ b = 14k/4 = 7k/2 ∴ BO /OF = c+a / b = 10k+9k / 7k/2 = 19 Х 2/ 7 = 38/7 Hence BO / OF = 38/7

दी गयी आकृति में, त्रिभुज ABC का अंत: केंद्र 0 है। यदिAO 5 Om CO 32 -7 = = तथा 6 = , है, तो BO/OF का मान क्या है ?ABEC

Answer»

Solution

Construction:

Draw : AE ⊥ BC

Draw; BF ⊥ AC

Draw : DC ⊥ AB

O is the intersection point .

Given That: AO /OE = 5/4 and OC /OD = 3/2

Let BC = a, CA = b, and AB = c

∴AO/OE = b+c/a = OC/OD = b+c/c

∴ b+c/a = 5/4 ⇒b+c+a/a = 5+4/4 = 9/4 -----(1)

and b+a/ c = 3/2

∴ a+b+c/c = 3+2/2 = 5/2 --(2)

on Dividing eq. (2) by (1) we get.

a/c = 5/2 Χ 4/9 = 10/9

⇒ a = 10k

and c = 9k

⇒ b = 14k/4 = 7k/2

∴ BO /OF = c+a / b = 10k+9k / 7k/2 = 19 Х 2/ 7 = 38/7

Hence BO / OF = 38/7