In this post, you will find the NCERT solutions for class 10 maths ex 10.1. These solutions are based on the latest syllabus of NCERT Maths class 10.
NCERT Solutions for Class 10 Maths Ex 10.1
1.
How many tangents can a circle have?
Answer: Since
there are infinitely many points on the circumference of a circle and at each
point we can draw a unique tangent, therefore, a circle can have infinitely
many tangents.
2.
Fill in the blanks:
(i)
A tangent to a circle intersects it in one
point(s).
(ii)
A line intersecting a circle in two points is called a secant.
(iii) 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 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
Solution: (D) Since, PQ is
the tangent and OP is the radius through the point of contact.
Therefore, ∠OPQ = 90°
[Since, the tangent at any point of a circle
is perpendicular to
the radius through the point of contact.]
OQ2 = OP2 + PQ2 [By Pythagoras theorem]
(12)2 = (5)2 + (PQ)2
144 = 25 + PQ2
PQ2 = 144 – 25 = 119
PQ = √119 cm
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.
Solution:
