RD Sharma Solutions Class 10 Maths Chapter 10 Circles

RD Sharma Solutions for Class 10 Maths Chapter 10 – Circles offered by Infinity Learn provide precise and easy-to-understand answers, designed to enhance students’ learning skills. Preparing for crucial exams like the Class 10 board exams requires the right resources, and Infinity Learn brings everything under one roof. For Maths preparation, RD Sharma Solutions serve as the perfect practice companion, offering well-structured answers aligned with the latest CBSE Syllabus.

Chapter 10, Circles, in RD Sharma Class 10 Solutions, includes two exercises focusing on important topics such as:

• Properties of tangents to a circle
• Length of tangents drawn from a point
• Tangents to intersecting circles
• Tangents to concentric circles
• Cyclic quadrilaterals and related concepts

The RD Sharma Solutions for Class 10 Circles guide students on how to approach these problems correctly and efficiently. They also introduce useful tricks and shortcuts, helping students solve problems faster and with greater accuracy.

For strong conceptual clarity, it’s essential that students practice these solutions regularly. Consistent practice not only improves problem-solving skills but also enhances time management, both of which are crucial for achieving high scores in CBSE board examinations.

Students can easily access the RD Sharma Class 10 Solutions for Circles in PDF format, available for both online and offline use through the provided links, making it convenient for anytime, anywhere learning.

Download RD Sharma For Class 10 Maths Chapter 10 Circles PDF Here

Access answers to Maths RD Sharma Solutions For Class 10 Chapter 10 – Circles

1. Fill in the blanks:

• (i) The common point of a tangent and a circle is called the point of contact.
• (ii) A circle can have two parallel tangents at most.
• (iii) A tangent touches the circle at exactly one point.
• (iv) A line that intersects a circle at two points is called a secant.
• (v) The angle between a tangent and the radius at the point of contact is 90°.

2. How many tangents can a circle have?

Solution: A circle can have an infinite number of tangents because a tangent can be drawn at every point on the circumference.

3. If a line intersects a circle at two points, what is it called?

Solution: It is called a secant.

4. What is the angle between a tangent and the radius at the point of contact?

Solution: The angle is always 90°.

5. Can a tangent intersect the circle at more than one point?

Solution: No, a tangent touches the circle at only one point.

6. If PT is a tangent to a circle with center O, OP = 17 cm and OT = 8 cm, find PT.

Solution: Using Pythagoras theorem:

OP² = OT² + PT²

17² = 8² + PT²

289 = 64 + PT²

PT² = 225

PT = √225 = 15 cm

7. Find the length of the tangent from a point 13 cm away from the center of a circle with radius 5 cm.

Solution:

Length = √(13² - 5²)

= √(169 - 25)

= √144

= 12 cm

8. A point P is 26 cm away from center O, and the length of the tangent from P to the circle is 10 cm. Find the radius.

Solution: Using Pythagoras theorem:

OP² = OT² + PT²

26² = OT² + 10²

676 = OT² + 100

OT² = 576

OT = √576 = 24 cm

9. Two tangents are drawn to a circle from an external point. What can be said about their lengths?

Solution: The two tangents drawn from an external point to a circle are always equal in length.

10. Find the length of the tangent from a point 25 cm away from the center of a circle with a radius of 7 cm.

Solution:

Length = √(25² - 7²)

= √(625 - 49)

= √576

= 24 cm

11. Define a cyclic quadrilateral.

Solution: A cyclic quadrilateral is a four-sided figure where all vertices lie on the circumference of a circle.

12. What is the sum of the opposite angles of a cyclic quadrilateral?

Solution: In a cyclic quadrilateral, the sum of the opposite angles is always 180°.

13. Can a triangle be inscribed in a circle?

Solution: Yes, every triangle can be inscribed in a circle. The circle that passes through all the vertices of a triangle is called the circumcircle.

14. Find the length of the tangent from a point 10 cm away from the center of a circle of radius 6 cm.

Solution: Length = √(10² - 6²)

= √(100 - 36)

= √64

= 8 cm

15. If two circles intersect at two points, what is the line joining these points called?

Solution: The line joining the points of intersection of two circles is called the common chord.