Question

1. O is any point in the interior of APOR, If PO - 7 cm, OR = 6 cm and PR = 5 cm,
prove that OP + 00 + OR > 9 cm.​

Answer 1

Answer: If three sides of triangle PQR is 6 cm, 7 cm & 5 cm and O is any point inside it then (OP+OQ+OR) > 9 cm.

Step-by-step explanation:

Referring to the figure attached below we have,

In ∆PQR,

PQ = 6 cm

QR = 7 cm

PR = 5 cm

Let O be any point inside the triangle and join OP, OQ & OR.

According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the measure of the third side.

Therefore,

In ∆POQ, [OP + OQ] > 6 cm ….. (i)

In ∆QOR, [OQ + OR] > 7 cm ….. (ii)

In ∆POR, [OP + OR] > 5 cm ……. (iii)

Now, adding eq. (i), (ii) & (iii), we get

[OP + OQ] + [OQ + OR] + [OP + OR] > [6 + 7 + 5] cm

⇒ 2 [OP + OQ + OR] > [18 cm]

⇒ [OP + OQ + OR] > [18/2] cm

⇒ [OP + OQ + OR] > 9 cm  

Hence proved