Study Materials and Revision Notes for Ch 10 Circle Class 10th Maths
Circle• Circle: A circle is a locus of a point which moves in such a way that the distance from that point is always fixed.
• Radius: The constant distance from the centre to the circumference of the circle.
• Secant: A line which intersect the circle at two different points.
• Chord: Any line segment joining the two points on the circumference of the circle.
• Diameter: The longest distance between the two points on the circumference of the circle. It is the longest chord.
Here, AO is the radius of the circle and AB is the diameter of the circle.
• Tangent: A line which touches the circle exactly at one point.
• For cubic polynomial: If α,β and γ are zeroes of polynomial p(x) = ax3 + bx2 + cx + d then:
(i) α + β + γ = -b/a = (-coefficient of x2)/(coefficient of x3)
(ii) αβ + βγ + γα = c/a = (constant term of x)/(coefficient of x3)
(iii) α.β.γ = -d/a = (-constant term)/(coefficient of x3)
(iv) A cubic polynomial whose zeroes are α, β and γ, is given by:
p(x) = k[x3 - (α+β+γ)x2 + (αβ+βγ+γα)x - αβγ] where k is any real number.
• Division Algorithm: If p(x) and g(x) are any two polynomials where g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that:
p(x) = g(x) × q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).
(i) α + β + γ = -b/a = (-coefficient of x2)/(coefficient of x3)
(ii) αβ + βγ + γα = c/a = (constant term of x)/(coefficient of x3)
(iii) α.β.γ = -d/a = (-constant term)/(coefficient of x3)
(iv) A cubic polynomial whose zeroes are α, β and γ, is given by:
p(x) = k[x3 - (α+β+γ)x2 + (αβ+βγ+γα)x - αβγ] where k is any real number.
• Division Algorithm: If p(x) and g(x) are any two polynomials where g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that:
p(x) = g(x) × q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).