Circles — Class 9 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 9 Mathematics chapter "Circles" — 8 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 9 Mathematics chapter "Circles" — 8 important questions with detailed answers for CBSE board exam preparat…

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Key Questions Covered:

  1. Define a circle and state the following properties: (1) All radii of a circle…
  2. State the theorem about angles subtended by an arc at the center and on the c…
  3. In circle with center O and radius 5 cm, a chord AB is at a perpendicular dis…
  4. + 5 more questions in the full chapter

Solutions Summary:

Question Status
Define a circle and state the following properties: (1) A… ✓ Solved
State the theorem about angles subtended by an arc at the… ✓ Solved
In circle with center O and radius 5 cm, a chord AB is at… ✓ Solved

Showing 3 of 8 questions

Q1: Define a circle and state the following properties: (1) All radii of a circle are equal. (2) A chord is a line segment joining any two points on the circle. (3) The longest chord is the diameter. If a circle has radius 7 cm, find the diameter and the circumference.

Step 1: Definition of Circle: A circle is the locus of all points in a plane that are at a constant distance (radius) from a fixed point (center). Step 2: Properties: (1) All radii of a circle are equal: Since all points on the circle are equidistant from the center, all radii r are equal. (2) Chor...

Q2: State the theorem about angles subtended by an arc at the center and on the circumference: If an arc AB subtends an angle of 60° at the center O, what angle does the same arc subtend at a point C on the circumference (on the major arc)?

Step 1: Theorem: The angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any point on the circle (on the major arc). Angle at center = 2 × Angle at circumference Step 2: Given: Arc AB subtends angle AOB = 60° at center O Point C is on the major arc A...

Q3: In circle with center O and radius 5 cm, a chord AB is at a perpendicular distance of 3 cm from the center O. Find the length of chord AB.

Step 1: Given: Circle with center O and radius r = 5 cm Chord AB at perpendicular distance d = 3 cm from center O Step 2: Let M be the foot of the perpendicular from O to chord AB. Then OM ⊥ AB and OM = 3 cm Step 3: Important property: The perpendicular from the center of a circle to a chord bisec...

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