Area of circle given arc length?
- Pramod KumarLv 74 months ago
Answer : Option C is correct.
It can be clearly shown that --
The two circles have the same radius (r) and PS = ST = PR = RT
Also M is midpoint of RS so that MS = MR = r/2
Hence cos θ = MS/PS = (r/2) / r = 1/2
=> θ = 60° , therefore, Angle PST = 120°
Consider circle with center S :
Arc PRT subtends 120° at the center.
Hence its length PRT ( given = 2 π ) = (120/360) * 2 π r
=> r/3 = 1
=> r = 3
Hence area of the circle = π (3)² = 9 π ...................... Answer
- PuzzlingLv 74 months ago
PRS and RST have sides that are all equal to the radius, so they are both equilateral triangles.
The angles of an equilateral triangle are all 60° so angle PRT is 120° and the arc PRT is equal to 1/3 of a full circle.
The circumference of the full circle will be 6π which means the radius is 3.
C = 2πr = 6π --> r = 3
From that you can easily find the area:
A = πr²
A = 3² * π
A = 9π