Relationship between Radius of circle with tangent:
Theorem: The tangent at any point of a circle is perpendicular to the radius through the point of contact.
Given : A circle with center O. XY is a tangent and P is the point of contact. To Prove: OP is perpendicular to XY Construction: Take a point Q on XY join OQ. Proof: Now point Q lies outside the circle because the tangent just touches the circle at point P So as Q points lies on XY therefore it is outside the circle. OQ > radius of the circle [ Q is outside the circle] OQ > OP So any point on XY the distance from the center will be more than radius That is OP is the shortest of all the distances of the point O to the points on XY. So, OP is perpendicular to XY [ because the shortest distance is perpendicular] | I |
Illustration: A point P is 13 cm from the centre of the circle. The length of the tangent from P to the circle is 12 cm. Find the radius of the circle.
Solution Since the tangent to a circle is perpendicular to the radius through the point of contact,
It is given that OP = 13 cm, PT = 12 cm and let OT = r cm In right triangle OTP,
radius of the circle is 5 cm. |
PT is a tangent to a circle whose centre is O. If PT = 12 cm and PO = 13 cm then find the radius of the circle. | |||
Right Option : A | |||
View Explanation |
In the given figure, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If ∠POQ = 70, then ∠TPQ is equal to ______________ | |||
Right Option : B | |||
View Explanation |
In the figure, the pair of tangents AP and AQ, drawn from an external point A to a circle with centre O, are perpendicular to each other and length of each tangent is 4 cm, then the radius of the circle is __________________ | |||
Right Option : B | |||
View Explanation |
My experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
It was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
It 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.
Abhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
A 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.
It has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
My 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.
Abhyas 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.
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.
I 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