A) Solve the following (any 2)
6
1) 'C' is the centre of the circle, whose radius is 10cm. Find the distance of the chord from
the center if the length of the chord is 12 cm.
C 10 cm
12 cm
Answers
Given:
✰ C is the centre of the circle.
✰ Radius of a circle ( AC ) = 10 cm
✰ The length of the chord ( AB ) = 12 cm.
To find:
✠ The distance of the chord from the center.
Solution:
First we will find AD and then we know that ACD is a right angle triangle. Thus, by using Pythagoras theorem, we will find out CD that is the distance between the centre of the chord.
Let's find out...✧
C is the centre of the circle
Let AC be the radius of a circle and AB be the length of the chord.
Draw CD ⟂ AB
CD bisects AB
∴ AD = BD = 1/2 AB
➛ AD = 1/2 × 12
➛ AD = 12/2
➛ AD = 6 cm
In ∆ACD, ∟D is right angled triangle,
Thus, by using Pythagoras theorem,
➤ AC² = CD² + AD²
➤ 10² = CD² + 6²
➤ 100 = CD² + 36
➤ CD² = 100 - 36
➤ CD² = 64
➤ CD = √64
➤ CD = 8 cm
∴ The distance of the chord from the center = 8 cm
_______________________________
Given:
✰ C is the centre of the circle.
✰ Radius of a circle ( AC ) = 10 cm
✰ The length of the chord ( AB ) = 12 cm.
To find:
✠ The distance of the chord from the center.
Required Solution:
First we will find AD and then we know that ACD is a right angle triangle. Thus, by using Pythagoras theorem, we will find out CD that is the distance between the centre of the chord.
Let's find out...✧
C is the centre of the circle
Let AC be the radius of a circle and AB be the length of the chord.
Draw CD ⟂ AB
CD bisects AB
- ∴ AD = BD = 1/2 AB
- AD = 1/2 × 12
- AD = 12/2
- AD = 6 cm
In ∆ACD, ∟D is right angled triangle,
Thus, by using Pythagoras theorem,
- AC² = CD² + AD²
- 10² = CD² + 6²
- 100 = CD² + 36
- CD² = 100 - 36
- CD² = 64
- CD = √64
- CD = 8 cm
∴ The distance of the chord from the center = 8 cm
_______________________________