Perpendicular From Centre of Circle Bisects the Chord and Vice Versa
Perpendicular From Centre of Circle Bisects the Chord and Vice Versa
Theorem 1 The perpendicular from the centre of a circle to a chord bisects the chord.
Given A chord AB of a circle C (O,r) and perpendicular OD to the chord AB. TO PROVE AD = DB CONSTRUCTION Join OA and OB. PROOF In triangles AOD and BOD, we have and, So, by RHS - criterion of congruence, we have
Hence Proved |  |
Theorem 2: A line drawn from the centre of a circle to the mid point of the chord is perpendicular to the chord
Given A chord AB of a circle C (O,r) and a line OD which bisects the chord AB. TO PROVE OD is perpendicular to AB CONSTRUCTION Join OA and OB. PROOF In triangles AOD and BOD, we have and, So, by SSS - criterion of congruence, we have
But they are linear pairs so Hence Proved |  |
Illustration: If the length of a chord of a circle is 24 cm and is at a distance of 9 cm from the centre of the circle, Find the radius of the circle . The length of a chord of a circle AB = 24 cm Perpendicular distance from the centre OD = 9 cm As the perpendicular bisects the chord AD = 12 cm OA = 15 cm
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A chord of length 14 cm is at a distance of 6 cm from the centre of a circle. The length of another chord at a distance of 2 cm from the centre of the circle is | |||
| Right Option : D | |||
| View Explanation | |||
AB and CD are two parallel chords of a circle with centre O such that AB = 6 cm and CD = 12 cm. The chords are on the same side of the centre and the distance between them is 3 cm. The radius of the circle is _________________ | |||
| Right Option : D | |||
| View Explanation | |||
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| Right Option : D | |||||
| View Explanation | |||||
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About Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
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Hiya Gupta
8thWhen I have not joined Abhyas Academy, my skills of solving maths problems were not clear. But, after joining it, my skills have been developed and my concepts of science and SST are very well. I also came to know about other subjects such as vedic maths and reasoning.
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Barkha Arora
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Ayan Ghosh
8thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
Aman Kumar Shrivastava
10thThird consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...
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Prisha Gupta
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Eshan Arora
8thOne of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
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Cheshta
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Aman Kumar Shrivastava
10thIn terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...
Aman Kumar Shrivastava
10thWe started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.
Manya
8thMy experience with Abhyas academy is very nice or it can be said wonderful. I have been studying here from seven class. I have been completing my journey of three years. I am tinking that I should join Abhyas Academy in tenth class as I am seeing much improvement in Maths and English
Hridey Preet
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10thAbhyas academy is great place to learn. I have learnt a lot here they have finished my fear of not answering.It has created a habit of self studying in me.The teachers here are very supportive and helpful. Earlier my maths and science was good but now it has been much better than before.
