Question

Find the length of a chord which is at a distance of 4 m from the centre of a circle of radius 5 m​

Answer 1

⠀⠀⠀⠀⠀★ Required figure

⠀

We have,

• Radius = 5m
• Distance from the centre = 4m

⠀

Since, OC is a perpendicula bisector of AB (chord). Therefore, ∆OAC is a right angled triangle.

⠀

By using Pythagoras theorem

⠀

• OA² = 0C² + AC²

⠀

→ (5)² = (4)² + AC²

→ 25 = 16 + AC²

→ AC² = 25 - 16

→ AC² = 9

→ AC = √9

→ AC = 3 m

⠀

We know that OC is a bisector of AB, so we can say that

• AB = 2AC

⠀

→ AB = 2 × 3

→ AB = 6m

⠀

Hence,

• Length of the chord is 6m.