Maths Circle Presentation For Std.8 CBSE
- 1. Circle Presentation by Dev Jain (OE – 095) Std. 8 English Medium Teacher’s Name: Bharat Amarchedda
- 2. WHATIS A CIRCLE? In Maths or Geometry, a circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the centre. The distance from the centre of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.
- 3. AREA OF A CIRCLE Area of a circle is the region occupied by the circle in a two- dimensional plane. It can be determined easily using a formula, A = πr2, (Pi r-squared) where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, etc.
- 4. PARTS OF CIRCLE Parts of Circle Include: • Chord • Secant • Tangent • Arc • Sector • Segment
- 5. CHORD The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle. It should be noted that the diameter is the longest chord of a circle which passes through the center of the circle. The figure below depicts a circle and its chord.
- 6. SECANT A straight line that intersects a circle in two points is called a secant line. A chord is the line segment that joins two distinct points of the circle. A chord is in a unique secant line and every secant line defines a unique chord. In geometry, a secant is a line that cuts any curve in at least two different points. Secant means ‘to cut’ extracted from a Latin word ‘secare’. While in a circle, a secant will touch the circle in exactly two points and a chord is the line segment defined by these two points, that is the interval on a secant whose endpoints are these two points. If a secant and a tangent of a circle are drawn from a point outside the circle, then; Lengths of the secant × its external segment = (length of the tangent segment)2
- 7. TANGENT Tangent to a circle is the line that touches the circle at only one point. There can be only one tangent at a point to circle. Point of tangency is the point at which tangent meets the circle. Now, let’s prove tangent and radius of the circle are perpendicular to each other at the point of contact. Suppose a point P lies outside the circle. From that point P, we can draw two tangents to the circle meeting at point A and B. Now let a secant is drawn from P to intersect the circle at Q and R. PS is the tangent line from point P to S. Now, the formula for tangent and secant of the circle could be given as: PR/PS = PS/PQ PS2=PQ.PR
- 8. ARC The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc. An Arc is named based on its endpoints. The red arc in the above figure is called arc AB or BA since the order of points doesn’t matter. This can be expressed as the letter AB with a curved line above it, such as ABˆ and read as “arc AB”.
- 9. SECTOR A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. The most common sector of a circle is a semi-circle which represents half of a circle. A circle containing a sector can be further divided into two regions known as a Major Sector and a Minor Sector. In the figure below, OPBQ is known as the Major Sector and OPAQ is known as the Minor Sector. As Major represent big or large and Minor represent Small, which is why they are known as Major and Minor Sector respectively. In a semi-circle, there is no major or minor sector. Area of sector = θ360×πr2
- 10. SEGMENT A segment of a circle can be defined as a region bounded by a chord and a corresponding arc lying between the chord’s endpoints. In other words, a circular segment is a region of a circle which is created by breaking apart from the rest of the circle through a secant or a chord. We can also define segments as the parts that are divided by the circle’s arc and connected through a chord by the endpoints of the arc. It is to be noted that the segments do not contain the center point. There are two classifications of segments in a circle, namely the major segment and the minor segment.
- 11. I THANK ALLOF YOU FOR GOING THROUGHTHIS ENTIRE PRESENTATION. TAPOVAN VATSALYADHAM ENGLISH MEDIUM SCHOOL