CONSTRUCT THE TANGENT TO A CIRCLE AT A POINT OUTSIDE IT:
Case (a) : To draw the tangent to a circle at a given point on it, when the centre of the circle is known :
Required : To draw the tangent to the circle at P.
Steps of Construction:
(i) Take a point O as centre and draw a circle of given radius.
(ii) Take a point P on the circle.
(iii) Join OP.
(iv) Draw a line AB perpendicular to OP at the point P.APB is the required tangent at P.
Case (b) : To draw the tangent to a circle at a given point on it, when the centre of the circle is not known.
Given : A circle and a point P on it.
Required : To draw the tangent to the circle at P.
Steps of Construction:
(i) Draw any chord PQ through P and join P and Q to a point R in major arc PQ (or minor arc PQ).
(ii) COnstruct equal to and on opposite side of R with respect to chord PQ.
Produce BP to A to get the required tangent APB
CONSTRUCTION OF A TANGENT TO A CIRCLE FROM A POINT OUTSIDE THE CIRCLE:
In this situation, when the point lies outside the circle, there will be two tangents to the circle from this point.
In this construction, again we have two different situations:
Case (a) : To draw the tangent to a circle from a point outside it (external point), when its centre is known.
Given : A circle with centre O and a point P outside it.
Required: To construct the tangents to the circle from point P.
Steps of Construction:
(i) Join OP and bisect it. Let M be the mid-point of OP.
(ii) Taking M as centre and MO as radius, draw a circle which intersect the given circle in two points, say A and B.
(iii) Join PA and PB. These are the required tangents from P to given circle.
Example : Draw a circle of radius 2.5 cm. From a point P, 6 cm. apart from the centre of the circle, draw two tangents to the circle.
SOLUTIONS:
Given : A point P is at a distance of 6 cm. From the centre of a circle or radius 2.5 cm.
Required : To draw two tangents to the circle from the given point P.
Steps of construction:
(i) Draw a line segment OP of length 6 cm.
(ii) With centre O and radius equal to 2.5 cm, draw a circle.
(iii) Draw the right bisector of OP, intersecting OP at M. Let M be mid-point of OP.
(iv) Taking M as centre and MO as radius draw a circle which intersect the given circle in two points, say A and B.
(v) Join PA and PB. These are the required tangents from P to the given circle.
Steps of construction :
(i) Let P be the external point from where the tangents are to be drawn to the given circle. Through P draw a secant PAB to intersect the circle at A and B (say).
(ii) Produce AP to a point C such that AP = PC i.e., P is the mid-point of AC.
(iii) Draw a semi-circle with BC as diameter.
(iv) Draw intersecting the semi-circle at D.
(v) With P as centre and PD as radius draw arcs to intersect the given circle at T and T1.
(vi) Join PT and PT1. Then PT and PT1 are the required tangents.
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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
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When 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.
Third 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 ...
Abhyas 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...
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.
My 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
Usually 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...
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.
We 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.
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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.