Length of Tangents to a Circle
Length of Tangents to a Circle
Length of Tangents to a Circle: it is the distance of the point P to the point of contact on the circle that is point A and Point B. Or in other words PA and PB are the lengths on tangent from point P to the circle
Theorem: The length of tangents drawn from an external point to a circle are equal. Given :A circle with centre O. PA and PB to tangents from point P. To Prove: PA = PB Proof: Join OA an OB In OA = OB [radii of the same circle] OP = OP [ common ] Thus PA = PB [CPCT] Thus, lengths of tangents from an external point to a circle are equal. Corollary: Theline joining the centre of the circle and the external point i.e. OP is the angle bisector of As
Similarly OP is the angle bisector of |  |
ILLUSTRATION : A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD =AD + BC
Solution A quadrilateral ABCD circumscribes a cricle. Since the lengths of tangents from an external point to a circle are equal, we get AP = AS [ lengths of tangents from point A ] BP = BQ [ lengths of tangents from point B ] CR = CQ [ lengths of tangents from point C ] DR = DS [ lengths of tangents from point D ] Adding the above expressions, we get AP + BP + CR + DR = AS + BQ + CQ + DS
Hence Proved |  |
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In 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...
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10thOne 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.
Aman Kumar Shrivastava
10thUsually we see institutes offering objective based learning which usually causes a lag behind in subjective examinations which is the pattern followed by schools. I think it is really a work of planning to make us students grab the advantages of modes of examination, Objective Subjective and Onli...
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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.
Sharandeep Singh
7thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
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Aman Kumar Shrivastava
10thIt was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
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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Ayan Ghosh
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Hiya Gupta
8thAbout 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.
Shreya Shrivastava
8thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thMy experience with Abhyas Academy has been very good. When I was not in Abhyas whenever teacher ask questions I could not speak it confidently but when I came in Abhyas, my speaking skills developed and now I am the first one to give the answer of teachers question.
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7thI have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
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10thThe experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confidence to overcome competitive exams. One of the best institutes for secondary education.
Aman Kumar Shrivastava
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Prisha Gupta
8thMy experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thAbhyas 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.
