Gujarat Board Solutions Class 10 Maths Chapter 10 Circles Ex 10.1

Gujarat Board Solutions Class 10 Maths Chapter 10 Circles Ex 10.1

Gujarat Board Textbook Solutions Class 10 Maths Chapter 10 Circles Ex 10.1

Question 1.
How many tangents can a circle have?
Solution:
Infinite many tangents. As there are infinitely many points on a circle and all the points can have its tangent.

Question 2.
Fill in the blanks:

1. A tangent to a circle intersects it in …………. point(s).
2. A line intersecting a circle in two points is called a ……….
3. A circle may have ……….. parallel tangents at the most.
4. The common point of a tangent to a circle and the circle is called ……….

Solution:

1. one
2. secant
3. two
4. point of contact

Question 3.
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the center O at a point Q so that OQ = 12 cm. Length PQ is
(a) 12 cm
(b) 13cm
(c) 8.5 cm
(d) 19 cm
Solution:
(d)

From figure,
∠OPQ = 900 (Theorem 10.1)
∴ ΔOPQ is a right-angled triangle.
Using Pythagoras theorem,
OP² + PQ² = OQ²
5² + PQ² = 12²
PQ² = 144 – 25 = 119
∴ PQ = √119 cm

Question 4.
Draw a circle and two lines parallel to a given line such that one is tangent and other, a secant to the circle.
Solution:
1. Draw a circle with center O.
2. Draw a line AB passing through O.
3. Draw a perpendicular bisector CD of AB.
4. From D, draw ∠ODF = 90°.
5. Take a point G on OD and draw ∠OGY = 90°.
∴ XY is a secant and EF is a tangent and AB || XY || EF.

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