Question

in figure, O is the centre of the circle and AB is the chord. If OD perpendicular on AB then find the radius.
AB = 6cm OD = 4cm

Answer 1

Solution :-

Given -

AB = 6 cm, OD = 4 cm and O is the center of the circle.

AB is a chord and OD is perpendicular to AB.

OA = Radius = ?

It is clear from the figure that AD = DB = 1/2 of AD

⇒ 1/2 × 6

⇒ AD = 3 cm

Now, using Pythagoras Theorem - 

⇒ (Hypotenuse)² = (Base)² + (Perpendicular)²

⇒ (OA)² = (AD) + (OD)²

⇒ (OA)² = (3)² + (4)²

⇒ (OA)² = 9 + 16

⇒ (OA)² = 25

⇒ OA = √25

⇒ OA = 5 cm

So, the radius of the circle is 5 cm

Answer.

Answer 2

Given -

AB = 6 cm, OD = 4 cm and O is the center of the circle.

AB is a chord and OD is perpendicular to AB.

OA = Radius = ?

It is clear from the figure that AD = DB = 1/2 of AD

⇒ 1/2 × 6

⇒ AD = 3 cm

Now, using Pythagoras Theorem - 

⇒ (Hypotenuse)² = (Base)² + (Perpendicular)²

⇒ (OA)² = (AD) + (OD)²

⇒ (OA)² = (3)² + (4)²

⇒ (OA)² = 9 + 16

⇒ (OA)² = 25

⇒ OA = √25

⇒ OA = 5 cm

So, the radius of the circle is 5 cm

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