Circles: class 10
Circle: A figure made by all the points which are at the same distance from a fixed
point is called a Circle.
Center: The fixed point is known as the centre of the circle.
Radius: The distance from any point on the circle to the fixed point is the radius.
Any line segment which joins the centre and any point on the circle is known as
the Radius.
Diameter: Diameter is two times the radius. It is the longest chord on the circle
which passes through the centre. All the diameters have the same length.
Chord: Any line segment made by joining any two points on the boundary of the
circle is called Chord.
Circumference: The length of the boundary of the circle is called the
circumference of the circle.
Arc: An arc is the part of the circle joining two points on the circumference of the
circle.
Sector: An area made by an arc and two radii of the circle, by joining the centre to
the endpoints of the arc is called Sector.
Segment: An area made by a chord and an arc of the circle is called Segment.
, Tangent to a Circle
All the tangents of a circle are perpendicular to the radius through the point of
contact of that tangent.
O
X Y
P Q
OP is the radius of the circle and Q is any point on the line XY which is the tangent
to the circle. As OP is the shortest line of all the distances of the point O to the
points on XY. So OP is perpendicular to XY. Hence, OP⊥ XY
Example
Find the radius of the circle in the given figure, if the length of the tangent from
point A which is 5 cm away from center is 4 cm.
Solution
As we know that the radius is perpendicular to the radius, so the ∆ABO is a right
angle triangle.
Given, AO = 5 cm and AB = 4 cm
We can use Pythagoras theorem here
OA2 = OB2 + AB2
OB2 = OA2 - AB2
= 52 - 42
= 25 – 16
OB2 = 9
OB = 3
So the radius of the given circle is 3 cm
Number of Tangents from a Point on a Circle
1. There could be only one tangent at one point of contact.
Circle: A figure made by all the points which are at the same distance from a fixed
point is called a Circle.
Center: The fixed point is known as the centre of the circle.
Radius: The distance from any point on the circle to the fixed point is the radius.
Any line segment which joins the centre and any point on the circle is known as
the Radius.
Diameter: Diameter is two times the radius. It is the longest chord on the circle
which passes through the centre. All the diameters have the same length.
Chord: Any line segment made by joining any two points on the boundary of the
circle is called Chord.
Circumference: The length of the boundary of the circle is called the
circumference of the circle.
Arc: An arc is the part of the circle joining two points on the circumference of the
circle.
Sector: An area made by an arc and two radii of the circle, by joining the centre to
the endpoints of the arc is called Sector.
Segment: An area made by a chord and an arc of the circle is called Segment.
, Tangent to a Circle
All the tangents of a circle are perpendicular to the radius through the point of
contact of that tangent.
O
X Y
P Q
OP is the radius of the circle and Q is any point on the line XY which is the tangent
to the circle. As OP is the shortest line of all the distances of the point O to the
points on XY. So OP is perpendicular to XY. Hence, OP⊥ XY
Example
Find the radius of the circle in the given figure, if the length of the tangent from
point A which is 5 cm away from center is 4 cm.
Solution
As we know that the radius is perpendicular to the radius, so the ∆ABO is a right
angle triangle.
Given, AO = 5 cm and AB = 4 cm
We can use Pythagoras theorem here
OA2 = OB2 + AB2
OB2 = OA2 - AB2
= 52 - 42
= 25 – 16
OB2 = 9
OB = 3
So the radius of the given circle is 3 cm
Number of Tangents from a Point on a Circle
1. There could be only one tangent at one point of contact.
