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Lesson Posted on 18 Aug Circles

Basics of Circle

Raj Kumar

I am Six Sigma Black belt trained from American Society of Quality I am 2011 pass out in B.tech from...

The equation of a circle with its centre at C(x0, y0) and radius r is: (x – x0)2 + (y – y0)2 = r2 If x = y0 = 0 (i.e. the centre of the circle is at origin) then equation of the circle reduce to x2 + y2 = r2. If r = 0 then the circle represents a point or a point... read more

Components of Circle

The equation of a circle with its centre at C(x0, y0) and radius r is:

(x – x0)2 + (y – y0)2 = r2   

              

If x = y0 = 0 (i.e. the centre of the circle is at origin) then equation of the circle reduce to x2 + y2 = r2.   

If r = 0 then the circle represents a point or a point circle.

The equation x2 + y2 + 2gx + 2fy + c = 0 is the general equation of a circle with centre

(–g, –f) and radius √(g2+f2-c).

              

Equation of the circle with points P(x1, y1) and Q(x2, y2) as extremities of a diameter is

(x – x1) (x – x2) + (y – y1)(y – y2) = 0. 

              

For general circle, the equation of the chord is x1x + y1y + g(x1 + x) + f(y1 +y) + c = 0

 

 For circle x2 + y2 = a2, the equation of the chord is x1x + y1y = a2

 

              

 

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Answered on 05/12/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

Find the length of the tangent from a point which is at a distance of 5 cm from the centre of the circle of radius 3 cm?

Tanay Likhar

Math Mentor

So, if you draw a circle it will form a right angle triangle with hypotenuse 5 cm and base 3 cm. using Pythagoras theorem, the length will be equal to 4 cm.
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Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

What is the distance of AB from the centre of the circle if AD is a diameter of a circle and AB is a... read more
What is the distance of AB from the centre of the circle if AD is a diameter of a circle and AB is a chord and AD = 34 cm, AB = 30 cm? read less

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Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then what is the radius of the circle passing... read more
If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then what is the radius of the circle passing through the points A, B and C? read less

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Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

What is the angle of BAC if ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing... read more
What is the angle of BAC if ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC is 140 degree? read less

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Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

If non-parallel sides of a trapezium are equal, prove that it is circle?

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Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to... read more
If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord? read less

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Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre?

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Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

What do you mean by tangents of a circle?

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Asked on 29/10/2016 CBSE/Class 10/Mathematics Tuition/Class IX-X Tuition Circles

What do you mean by Chords of a circle?

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