PSEB Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1
PSEB Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1
PSEB 10th Class Maths Solutions Chapter 10 Circles Ex 10.1
Question 1.
How many tangents can a circle have?
Solution:
Since at any point on a circle, there can be one and only one tangeni. But circle is a collection of infinite points, so we can draw infinite number of tangents to a circle.
Question 2.
Fill in the blanks:
(i) A tangent to a circle intersects it in ………………. point(s).
Solution:
one
(ii) A line intersecting a circle in two points is called a ………………..
Solution:
secant.
(iii) A circle can have ……………. parallel tangents at the most.
Solution:
two
(iv) The common point of a lingent h, circle and the circit is called ………………
Solution:
point of contact.
Question 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:
According to given information we draw the figure such that,
OP = 5 cm and OQ = 12 cm
∵ PQ is a tangent and OP is the radius
∵ ∠OPQ = 90°
Now, In right angled ∆OPQ.
By Pythagoras Theorem,
OQ2 = OP2 + QP2
Or (12)2 = (5)2 + QP2
Or QP2 = (12)2 – (5)2
Or QP2 = 144 – 25 = 119
Or QP = √119 cm.
Hence, option (D) is correct.
Question 4.
Draw a circle and two lines parallel to given line such that one is a tangent and other a secant to the circle.
Solution:
According to thc given information we draw a circle having O as centre and l is the given line.
Now, m and n be two lines parallel to a given line l such that m is tangent as well as parallel to l and n is secant to the circle as well as parallel to l.
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