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NCERT Class 10 Maths chapter 10 notes based on the circle, equation of circle graph of the circle, find radii of circle tangent and normal equation. The chapter circle Class 10 notes also includes how to draw a circle. CBSE Class 10 Maths chapter 10 notes include FAQ or frequently asked questions about the chapter. These topics can also be downloaded from Class 10 Maths chapter 10 notes pdf download.
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A circle is the locus of a point in a plane so that its distance from a fixed point in the plane is constant. The fixed point is called the centre of the circle and the constant distance is called the radius
Some results regarding circle
Position of a point with respect to a circle. Point P (x1, y1) lies outside, on, or inside a circle.
Here, r is the radius of the circle.
The point P is inside the circle when the distance is less than the radius. Then it is negative.
The point is outside the circle when the distance is greater than the radius. Then it is positive.
The point P is on the circle when distance and radius are equal. Then it is zero.
Equation of tangent to the circle x2+y2+2gx+2fy+c=0 from a point P (x1, y1)
xx1+yy1+g(x+x1)+f(y+y1)+c=0
It is the equation of the tangent.
An equation of the Normal to the circle x2+y2+2gx+2fy+c=0 from a point P (x1, y1)
x2+y2+2gx+2fy+c=0
(y-y1)/(y1+f)=(x-x1)/(x1+g)
It is the equation of normal.
S1=x2+y2+2g1x+2f1y+c1=0
S2=x2+y2+2g2x+2f2y+c2=0
S1-S2=0
(x-h)2+(y-k)2=r2
(x-h')2+(y-k')2=r'2
Case 1. When C1 C2 > r+r’ i.e., the distance between the centers is greater than the sum of their radii, the two circles do not intersect with each other and 4 common tangents can be drawn to two circles.
Here C1and C2 are the centres of two circles.
In this case, two circles either touch each other externally or internally.
Case 2. When C1 C2 = r+r’ i.e., the distance between the centers is equal to the sum of the radii, the two circles touch each other externally, two direct common tangents are real and distinct and the transverse common tangents coincide.
Case 3. When C1 C2 < r+r’ i.e the distance between the centres is less than the sum of the radii, the circles intersect at two real and distinct points, the two direct common tangents are real and distinct while the transverse common tangents are imaginary.
Circle Class 10 notes will be helpful to revise the chapter and to get an idea about the main topics covered in the chapter. CBSE Class 10 Maths chapter 10 notes also contain previous year’s questions and NCERT TextBook pdf. Circle Class 10 notes pdf download can be used to prepare in offline mode. Class 10 Maths chapter 10 notes contain frequently asked questions of the chapter.
Let there be a circle with a centre at O and diameter AB. At A, CD is the tangent to the circle and at B, EF is
the tangent to the circle. We shall prove that CD EF. Now, OA ⟂ CD and OB ⟂ EF [radius of the circle is
perpendicular to the tangent at the point of contact] Hence, between CD and EF, the alternate interior
angles are equal (is of 90o). ⇒ CD EF [if the alternate angles are equal then lines are parallel].
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