by Tiwari Academy
NCERT Solutions for Class 9 Maths Chapter 9 Exercise 9.2 Circles updated for new academic session 2024-25. Students can get here Class 9 Maths Ex. 9.2 in Hindi and English Medium based on revised syllabus and new NCERT textbooks for CBSE and State Boards 2024-25.
Class 9 Maths Exercise 9.2 Questions in Detail
- Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.
- If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.
- If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chords.
- If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD.
- Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6m each, what is the distance between Reshma and Mandip?
- A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.
| Class: 9 | Mathematics |
| Chapter: 9 | Exercise: 9.2 |
| Chapter Name: | Circles |
| Content Type: | PDF, Videos and Text format |
| Session: | CBSE 2024-25 |
| Medium: | Hindi and English Medium |
Theorems for Exercise 9.2 Solutions
Before venturing into next chapter we should know that we need to learn theorems from NCERT solutions Maths for class 9th states that chords of equal length of a given circle or of a congruent circles are equidistant from the center (or centers). This is a simple theorem and you can verify by actually drawing a circle and drawing two chords of same lengths.
Use of theorems in Exercise 9.2
Theorem says, Chords which are equidistant from the center are equal in length. This is just the converse theorem 6. It is not a difficult theorem but slightly more in difficulty level compared to theorem 6.
Now based on these two theorems exercise 9.2 contains 6 questions. Out of which the first 3 are seemingly easy and the last three needs little practice and application as well.
Theorem make Exercise 9.2 simpler
The above theorems are based on some simple observations. For example – if you want to draw a shortest line from a particular point to a straight line, then you should draw a perpendicular from that point that straight line.
Practically speaking suppose you are crossing a road and there is a vehicle coming from one side. Then it is better to let the vehicle go by.
Importance of theorems in Geometry
But if you stuck in between then the shortest to route cross will be the perpendicular distance will be one end to another. Thus we see that geometry have practice application in life.
It is suggested that students revise the old theorems as much as possible because to prove the new theorems i.e., the theorems under consideration we should be familiar with the theorems learnt in the past.
