CLASS 10 MATHEMATICS
Ch 10 – CIRCLES
1. How many tangents can a circle have?
A circle can have infinite tangents to a circle.
We know that A circle is made up of infinite points which are at an equal distance from a point.
So there are infinite points on the Circumference of a circle,
Infinite tangents can be drawn from them.
2. Fill in the blanks:
(i) A tangent to a circle intersects it in
A tangent to a circle intersects it in one point(s).
(ii) A line intersecting a circle in two points
is called a ………….
A line intersecting a circle in two points is
called a secant.
(iii) A circle can have …………… parallel
tangents at the most.
A circle can have two parallel tangents at the most.
(iv) The common point of a tangent to a circle
and the circle is called …………
The common point of a tangent to a circle and the circle is called the point of contact.
3. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
(A) 12 cm
(B) 13 cm
(C) 8.5 cm
(D) √119 cm
In this figure,
the line OP is perpendicular to tangent PQ.
i.e. OP ⊥ PQ
Using Pythagoras theorem in triangle ΔOPQ,
Where Angle P = 90
i.e. (Hypotenuse)2= (base)2+ (perpendicular)2
OQ2 = OP2+PQ2
(12)2 = 52+PQ2
144 = 25 + PQ2
PQ2 = 144-25
PQ2 = 119
PQ = √119 cm
option D i.e. √119 cm is the length of PQ.
4. Draw a circle and two lines parallel to
a given line such that one is a tangent and the
other, a secant to the circle.
In the figure,
XY and AB are the two parallel lines.
The line segment AB is the tangent at point C
while the line segment XY is the secant.