#### Study Materials and Revision Notes for Ch 10 Circle Class 10th Maths

**Circle**

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__: A circle is a locus of a point which moves in such a way that the distance from that point is always fixed.__

*Circle**•*

__The constant distance from the centre to the circumference of the circle.__

*Radius:*•

__A line which intersect the circle at two different points.__

*Secant:*•

__Any line segment joining the two points on the circumference of the circle.__

*Chord:*•

*The longest distance between the two points on the circumference of the circle. It is the longest chord.*

__Diameter:__
Here, AO is the radius of the circle and AB is the diameter of the circle.

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__: A line which touches the circle exactly at one point.__

*Tangent*
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(i) α + β + γ = -b/a = (-coefficient of x

(ii) αβ + βγ + γα = c/a = (constant term of x)/(coefficient of x

(iii) α.β.γ = -d/a = (-constant term)/(coefficient of x

(iv) A cubic polynomial whose zeroes are α, β and γ, is given by:

p(x) = k[x

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p(x) = g(x) × q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).

__If α,β and γ are zeroes of polynomial p(x) = ax__*For cubic polynomial:*^{3 }+ bx^{2 }+ cx + d then:(i) α + β + γ = -b/a = (-coefficient of x

^{2})/(coefficient of x^{3})(ii) αβ + βγ + γα = c/a = (constant term of x)/(coefficient of x

^{3})(iii) α.β.γ = -d/a = (-constant term)/(coefficient of x

^{3})(iv) A cubic polynomial whose zeroes are α, β and γ, is given by:

p(x) = k[x

^{3}- (α+β+γ)x^{2}+ (αβ+βγ+γα)x - αβγ] where k is any real number.•

__: 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:__*Division Algorithm*p(x) = g(x) × q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).