Area of a Sector Formula: If a sector makes an angle θ (measured in radians) at the center, then the area of the sector of a circle = (θ× r2)÷ 2. Here, θ is in radians.Length of Chord Formula: It can be calculated if the angle made by the chord at the center and the ...
For a circle, the arc length formula is θ times the radius of a circle. The formulas are:Arc Length = θ× r (used for radians) Arc Length = θ× (π/180) × r (used for degrees)Where,L = Length of an Arc θ = Central angle of Arc r = Radius of the circle...
TheoremsShapesFormula Alternate Segment Theorem ∠x = ∠y and∠a = ∠b The central angle subtended by two points on a circle is always twice the inscribed angle subtended by those points. ∠BOC = 2∠BAC Angles in the same segment are congruent. ∠PRQ = ∠PSQ Angles in a semicircle are...
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If the angle θ is in radians, then The area of the sector = (θ/2) r 2 Sector angle of a circle θ = (180 x l )/ (π r ). Segment of circle and perimeter of segment: Here radius of circle = r , angle between two radii is ”θ” in degrees. Area of the segment of ci...
Measurement by arc length (radians) Formula: s = rθ s = arc length r = radius of the circleθ = measure of the central angle in radians Red arc: r = 2 and θ = 2π/3, so s = 4π/3 Blue arc: r = 2 and θ = 4π/3, so s = 8π/3See...
You can find thearc lengthusing the following formula: s = rθ The length arcsis equal to the radiusrtimes the central angleθin radians. Unit Circle Theunit circleis a circle with a radius equal to 1, centered on the origin (0, 0). It is used to calculate the cosine, sine, and...
Step 3: Write the formula for arc lengthThe arc length L of a circle can be calculated using the formula:L=r×θwhere r is the radius and θ is the angle in radians. Step 4: Set up the equations for arc lengthsLet L1 be the arc length of the first circle and L2 be the arc le...
There is a lengthy reason, but the result is a slight modification of the Sector formula:Area of Segment = θ − sin(θ)2× r2 (when θ is in radians)Area of Segment = ( θ × π360 − sin(θ)2)× r2 (when θ is in degrees)...