From a circle of radius 7 units, an arc length is cut by a chord of length 7 units. What is the arc length of the smaller portion (in units)?

Question

Accepted Answer

Given:
- Radius (r) = 7 units
- Chord length (c) = 7 units

Step 1: Find the central angle θ (in radians) subtended by the chord.

The chord length c is related to the radius r and the central angle θ by:

c = 2r sin(θ/2)

Substitute the values:
7 = 2 × 7 × sin(θ/2)
7 = 14 sin(θ/2)

sin(θ/2) = 7/14 = 1/2

Therefore,
θ/2 = π/6 (since sin(π/6) = 1/2)

So,
θ = π/3 radians

Step 2: Calculate the arc length of the smaller arc.

Arc length (L) = r × θ
L = 7 × (π/3) = (7/3)π units

Hence, the arc length of the smaller portion is (7/3)π units.

Answer

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