Question

In the given figure if OM is the bisector of angle XOY. Such that OL = 6cm & OM = 7.5cm , then find the length of MN

Answer 1

Given :

• OM is bisector of ∠XOY .
• OL = 6 cm
• OM = 7.5 cm

To find :

• Length of MN

Solution :

In ∆ MOL and ∆ MON

1. MO = MO (common)
2. ∠L = ∠N (Each 90° from the figure)
3. ∠MOL = ∠MON (OM bisects ∠XOY)

$\therefore$ ∆ MOL $\cong$ ∆ MON (AAS)

Hence , LM = MN (By CPCT) _____(1)

In ∆ MOL , using Pythagoras theorem

$\implies \boxed{\rm MO^2 = OL^2 + LM^2 }$

⇢7.5² = 6² + LM²

⇢LM² = 7.5² - 6²

⇢LM² = 56.25 - 36

⇢LM² = 20.25

⇢LM = √20.25

⇢LM = 4.5

$\therefore$ MN = LM = 4.5 cm (From equation one)

Answer 2

Answer:

4.5 cm

Answer is in the picture

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