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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Abhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are very helpful in solving the problems. The major advantages of the institute is extra classes for weak...
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.
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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.
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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...
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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 ...