### Shortcut Methods

**JEE Mains:**

**Find the area of the circle with radius ‘r’.**

Area = πr²

**Find the circumference of the circle with radius ‘r’.**

Circumference = 2πr

**Find the equation of the circle with center ‘(a, b)’ and radius ‘r’.**

(x - a)² + (y - b)² = r²

**Find the equation of the tangent to the circle with center ‘(a, b)’ and radius ‘r’ at the point ‘(x1, y1)’.**

y - y₁ = (x - x₁) * [(y₁ - b)/(x₁ - a)]

**Find the equation of the normal to the circle with center ‘(a, b)’ and radius ‘r’ at the point ‘(x1, y1)’.**

y - y₁ = [(x₁ - a)/(y₁ - b)] * (x - x₁)

**Find the length of the chord of the circle with center ‘(a, b)’ and radius ‘r’ that passes through the points ‘(x1, y1)’ and ‘(x2, y2)’.**

Length of chord = √((x₂ - x₁)² + (y₂ - y₁)²)

**Find the area of the sector of the circle with center ‘(a, b)’ and radius ‘r’ that is subtended by the central angle ‘θ’.**

Area of sector = (θ/360) * πr²

**Find the length of the arc of the circle with center ‘(a, b)’ and radius ‘r’ that is subtended by the central angle ‘θ’.**

Length of arc = (θ/360) * 2πr

**CBSE Board Exams:**

**Find the area of the circle with radius ‘r’.**

Area = πr²

**Find the circumference of the circle with radius ‘r’.**

Circumference = 2πr

**Find the equation of the circle with center ‘(a, b)’ and radius ‘r’.**

(x - a)² + (y - b)² = r²

**Find the equation of the tangent to the circle with center ‘(a, b)’ and radius ‘r’ at the point ‘(x1, y1)’.**

(x - x₁)² + (y - y₁)² = r²

**Find the equation of the normal to the circle with center ‘(a, b)’ and radius ‘r’ at the point ‘(x1, y1)’.**

2x(x - x₁) + 2y(y - y₁) = r²

**Find the length of the chord of the circle with center ‘(a, b)’ and radius ‘r’ that passes through the points ‘(x1, y1)’ and ‘(x2, y2)’.**

Length of chord = √((x₂ - x₁)² + (y₂ - y₁)²)

**Find the area of the sector of the circle with center ‘(a, b)’ and radius ‘r’ that is subtended by the central angle ‘θ’.**

Area of sector = (θ/360) * πr²

**Find the length of the arc of the circle with center ‘(a, b)’ and radius ‘r’ that is subtended by the central angle ‘θ’.**

Length of arc = (θ/360) * 2πr

**Find the area of the segment of the circle with center ‘(a, b)’ and radius ‘r’ that is subtended by the central angle ‘θ’.**

Area of segment = Area of sector - Area of triangle formed by radii and chord =(θ/360) * πr² - (1/2) * r² * sinθ