Question

In the given figure, O is the centre of the circle of radius 5cm. OM perpendicula to AB, ON perpendicular to CD and AB parallel to CD ,if AB=6cm , CD =8cm, find the length of MN​

Answer 1

Answer:

radius is 5 cm

AB=6cm

CD=8cm

MN=10

Answer 2

Given :-

In the given figure, O is the centre of the circle of radius 5cm. OM perpendicular to AB, ON perpendicular to CD and AB parallel to CD ,if AB=6cm , CD =8cm

To Find :-

Length of MN

Solution :-

Join A to O and C to O

Now, We will have two right triangles ΔAOM & ΔCON

In ΔAOM we have

AM = AB/2

⇒ AM = 6/2

⇒ AM = 3 cm

⇒ OA = 5 cm [Radius is 5 cm]

By using Pythagoras theorem

⇒ (OA)² = (AM)² + (MO)²

⇒ (5)² = (3)² + (MO)²

⇒ 25 = 9 + (MO)²

⇒ 25 - 9 = (MO)²

⇒ 16 = (MO)²

⇒ √16 = MO

⇒ 4 = MO

Now,

In ΔCON we have

CN = CD/2

⇒ CN = 8/2

⇒ CN = 4 cm

⇒ CO = 5 cm [Radius is 5 cm]

By using pythagoras theorem

⇒ (CO)² = (CN)² + (NO)²

⇒ (5)² = (4)² + (NO)²

⇒ 25 = 16 + (NO)²

⇒ 25 - 16 = (NO)²

⇒ 9 = (NO)²

⇒ √(9) = NO

⇒ 3 = NO

Now,

Length of MN = MO + NO

⇒ MN = 4 + 3

⇒ MN = 7 cm

∴ Length of MN is 7 cm