Question

draw a circle of 3cm radius and draw two tangets to it from a point that lie outside it from a point centre of the circle​

Answer 1

Answer:

Drawing a circle of diameter 6.4cm is child's play. Draw a circle with radius 3.2cm by standard compass. Let the centre be labelled O.

Draw a normal (line passing through the center) to the circle and mark point on the line distanced at 6.4cm from the centre. Let this point be D.

Draw perpendicular bisector of OD, find midpoint of OD, label it M & draw a circle with radius MD, centered at M.

This centre will intersect the original one in two points say A & B, and in this case new circle will also be congruent to original one.

Join DA and DB, those are the required tangents.

Answer 2

Answer:

Given: A point P is outside the circle of radius 3 cm.

Required: To draw two tangents to the circle from the point P, without the use of centre.

Steps of constructing

(i) Draw a circle of radius 3 cm.

(ii) Take a point P outside the circle and draw a secant PAB, intersecting the circle at A and B.

(iii) Produce AP to C such that AP = CP.

(iv) Draw a semicircle, wit CB as a diameter.

(v) Draw PD ^ AB, intersecting the semi-circle AT D.

(vi) With PD as radius and P as centre draw two arcs to intersect the given circle at T and T’.

(vii) Joint PT and PT’. Which are the required tangents.

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