Question

Radius of circle is 10 cm. There are two chords of length 16 cm each, What will be
distance of these chords from the centre of the circle?​

Answer 1

Given :

• Radius of Circle = 10cm
• Length of Chord = 16cm

To Find :

• Distance of these chords from the centre of the circle.

Solution :

⠀⟶⠀OR = OP = 10cm ⠀⠀⠀⠀⠀[Radius]

⠀⟶⠀PQ = RS = 16cm ⠀⠀⠀⠀⠀ [Chord]

Perpendicular drawn from the centre of the circle to the chord bisects the chord, therefore :

⠀⟶⠀PU = ½ × PQ

⠀⟶⠀PU = ½ × 16

⠀⟶⠀PU = 8cm

Applying Pythagoras theorem in ∆OUP :

⠀⟶⠀(OP)² = (OU)² + (PU)²

⠀⟶⠀(10)² = (OU)² + (8)²

⠀⟶⠀100 = (OU)² + 64

⠀⟶⠀100 - 64 = (OU)²

⠀⟶⠀36 = (OU)²

⠀⟶⠀√36 = OU

⠀⟶⠀6cm = OU

Now, Congruent chords of the circle are equidistant from the circle therefore :

⠀⟶⠀OU = OT = 6cm

⛬ The distance of the Chord from the centre is 6cm.

___________________

Answer 2

Given:

Radius of Circle = 10cm

Length of Chord = 16cm

To find:

Distance of these chords from the centre of the circle.

Solution:

⠀⟶⠀OR = OP = 10cm ⠀⠀⠀⠀⠀[Radius]

⠀⟶⠀PQ = RS = 16cm ⠀⠀⠀⠀⠀ [Chord]

Perpendicular drawn from the centre of the circle to the chord bisects the chord, therefore :

⠀⟶⠀PU = ½ × PQ

⠀⟶⠀PU = ½ × 16

⠀⟶⠀PU = 8cm

Applying Pythagoras theorem in ∆OUP :

⠀⟶⠀(OP)² = (OU)² + (PU)²

⠀⟶⠀(10)² = (OU)² + (8)²

⠀⟶⠀100 = (OU)² + 64

⠀⟶⠀100 - 64 = (OU)²

⠀⟶⠀36 = (OU)²

⠀⟶⠀√36 = OU

⠀⟶⠀6cm = OU

Now, Congruent chords of the circle are equidistant from the circle therefore :

⠀⟶⠀OU = OT = 6cm

⛬ The distance of the Chord from the centre is 6cm.

___________________

Hope it will helps you ❤️