Question

A chord of length 16 centimetre is drawn in a circle of diameter 20 CM calculate its distance from the centre of the circle

Answer 1

✬ Distance of Chord = 6 cm ✬

Step-by-step explanation:

Given:

• Length of chord is 16 cm.
• Diameter of chord is 20 cm.

To Find:

• What is the distance of chord from centre of circle ?

Solution: Let in circle

• XY = chord of 16 cm
• XZ = Diameter of 20 cm
• O = Centre of circle
• OA = Distance of chord from O

[ Diameter is 20 cm so radius will be ]

➨ Radius = XO = OZ = 20/2

➨ Radius = 10 cm

As we know that , Perpendicular to the chord from the centre of circle bisects the chord in to two equal parts.

➼ XA = 1/2 of XY

➼ XA = 1/2 $\times$ 16

➼ XA = 8 cm

Now, in right angled triangle OAX,

• OA = Perpendicular
• XA = Base {16 cm}
• XO = Hypotenuse {10 cm}

Applying Pythagoras Theorem in ∆OAX

★ H² = P² + Base² ★

$\implies{\rm }$ XO² = OA² + XA²

$\implies{\rm }$ 10² = OA² + 8²

$\implies{\rm }$ 100 = OA² + 64

$\implies{\rm }$ 100 – 64 = OA²

$\implies{\rm }$ 36 = OA²

$\implies{\rm }$ √36 = OA

$\implies{\rm }$ √6 $\times$ 6 = OA

$\implies{\rm }$ 6 = OA

Hence, the distance of chord from centre of circle is 6 cm.

Answer 2

Distance of Chord = 6 cm ✬

Step-by-step explanation:

Given:

Length of chord is 16 cm.

Diameter of chord is 20 cm.

To Find:

What is the distance of chord from centre of circle ?

Solution: Let in circle

XY = chord of 16 cm

XZ = Diameter of 20 cm

O = Centre of circle

OA = Distance of chord from O

[ Diameter is 20 cm so radius will be ]

➨ Radius = XO = OZ = 20/2

➨ Radius = 10 cm

As we know that , Perpendicular to the chord from the centre of circle bisects the chord in to two equal parts.

➼ XA = 1/2 of XY

➼ XA = 1/2 \times× 16

➼ XA = 8 cm

Now, in right angled triangle OAX,

OA = Perpendicular

XA = Base {16 cm}

XO = Hypotenuse {10 cm}

Applying Pythagoras Theorem in ∆OAX

★ H² = P² + Base² ★

\implies{\rm }⟹ XO² = OA² + XA²

\implies{\rm }⟹ 10² = OA² + 8²

\implies{\rm }⟹ 100 = OA² + 64

\implies{\rm }⟹ 100 – 64 = OA²

\implies{\rm }⟹ 36 = OA²

\implies{\rm }⟹ √36 = OA

\implies{\rm }⟹ √6 \times× 6 = OA

\implies{\rm }⟹ 6 = OA

Hence, the distance of chord from centre of circle is 6 cm.