Seshu cheera

✅ Class 10 Maths Chapter 12: Areas Related to Circles 📚 Chapter Overview: This chapter helps students apply the properties of circles to find the area and perimeter (circumference) of sectors , segments , and composite figures involving circles. It blends geometry and mensuration skills for real-life applications. 🧠 Key Concepts, Formulas, and Theorems: 🔹 1. Circle: A closed two-dimensional figure where all points are equidistant from a fixed point (center). Radius (r): Distance from center to any point on the circle. Diameter (d): Twice the radius, i.e., d = 2 r d = 2r Circumference: Total boundary length of the circle Circumference = 2 π r \text{Circumference} = 2\pi r 🔹 2. Area of a Circle: Area = π r 2 \text{Area} = \pi r^2 Where π = 22 7  or  3.14 \pi = \frac{22}{7} \text{ or } 3.14 🔹 3. Sector of a Circle: A sector is a portion of a circle enclosed by two radii and the arc between them. Area of Sector : θ 360 ∘ × π r 2 \frac{\th...

  Class 10 CBSE Maths – Chapter 7: Coordinate Geometry 🔹 Key Concepts and Formulas ✅ Coordinate Plane A plane with two perpendicular lines (axes): x-axis (horizontal) and y-axis (vertical) The point of intersection is called the origin (0, 0) Coordinates are written as (x, y) ✅ Quadrants I Quadrant: (+x, +y) II Quadrant: (–x, +y) III Quadrant: (–x, –y) IV Quadrant: (+x, –y) ✅ Distance Formula To find distance between two points A ( x 1 , y 1 ) A(x_1, y_1) and B ( x 2 , y 2 ) B(x_2, y_2) : A B = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ✅ Section Formula To find coordinates of a point P which divides the line segment AB in the ratio m : n m:n : P = ( m x 2 + n x 1 m + n , m y 2 + n y 1 m + n ) P = \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right) ✅ Midpoint Formula Special case of section formula when m = n: Midpoint = ( x 1 + x 2 2 , y 1 + y 2 2 ) \text{Midpoint} = \left( \frac{x_1 + ...