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Ex-16.1, Circles, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics PDF Download

Q1) Fill in the blanks:

(i) All points lying inside/outside a circle are called ______ points/_______ points.

Solution:  Interior/Exterior

 

(ii) Circle having the same centre and different radii are called _____ circles.

Solution: Concentric

 

(iii) A point whose distance from the center of a circle is greater than its radius lies in _________ of the circle.

Solution: The Exterior

 

(iv) A continuous piece of a circle is _______ of the circle.

Solution: Arc

 

(v) The longest chord of a circle is a ____________ of the circle.

Solution: Diameter

 

(vi) An arc is a __________ when its ends are the ends of a diameter.

Solution: Semi circle

 

(vii) Segment of a circle is a region between an arc and _______ of the circle.

Solution: Center

 

(viii) A circle divides the plane, on which it lies, in _________ parts.

Solution: Three 

 

Q2) Write the truth value (T/F) of the following with suitable reasons:

(i) A circle is a plane figure.

Solution: T

 

(ii) Line segment joining the center to any point on the circle is a radius of the circle,

Solution: T

 

(iii) If a circle is divided into three equal arcs each is a major arc.

Solution: T

 

(iv) A circle has only finite number of equal chords.

Solution: F

 

(v) A chord of a circle, which is twice as long as its radius is the diameter of the circle.

Solution: T

 

(vi) Sector is the region between the chord and its corresponding arc.

Solution: T

 

(vii) The degree measure of an arc is the complement of the central angle containing the arc.

Solution: F

 

(viii) The degree measure of a semi-circle is 1800.

Solution: T

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FAQs on Ex-16.1, Circles, Class 9, Maths RD Sharma Solutions - RD Sharma Solutions for Class 9 Mathematics

1. What are the properties of a circle?
Ans. A circle has several properties: - All points on the circle's circumference are equidistant from the center of the circle. - The diameter of a circle is twice the length of its radius. - The circumference of a circle can be found using the formula C = 2πr, where r is the radius. - The area of a circle can be found using the formula A = πr², where r is the radius. - A tangent to a circle is a line that touches the circle at only one point.
2. How do you find the equation of a circle?
Ans. The equation of a circle can be found using the coordinates of its center (h, k) and its radius r. The general form of the equation is (x - h)² + (y - k)² = r². By substituting the values of h, k, and r into this equation, you can find the specific equation of the circle.
3. How do you find the length of an arc in a circle?
Ans. To find the length of an arc in a circle, you need to know the measure of the central angle (θ) that the arc subtends. The length of the arc can be calculated using the formula L = (θ/360) × 2πr, where r is the radius of the circle.
4. What is the relationship between the radius and diameter of a circle?
Ans. The diameter of a circle is always twice the length of its radius. Mathematically, the relationship between the radius (r) and diameter (d) is expressed as d = 2r.
5. How do you find the area of a sector in a circle?
Ans. To find the area of a sector in a circle, you need to know the measure of the central angle (θ) that the sector subtends. The area of the sector can be calculated using the formula A = (θ/360) × πr², where r is the radius of the circle.
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