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प्रश्न
Draw a circle at a radius of 4 cm. Take a point on it. Without using the centre at the circle, draw a tangent to the circle at point P.
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उत्तर
Steps of Construction:
(i) Draw a chord PQ through the given point on the circle.
(ii) Take a point R on the circle and join P and Q to a point R.
(iii) Construct ∠ QPY = ∠ PRQ on the opposite sides of the chord PQ.
(iv) Produce YP to X' to get YPX as the required tangent.
Construct a tangent to the circle from an external point:
In this section we shall study the construction at tangent to a circle from an external point when its center is; (i) Know (ii) Unknown
Type (I). Construction at tangent to a circle from an external point when its centre is known.
Steps of Construction:
(i) Join the centre O of the circle to the given external point P i.e., join OP.
(ii) Draw right bisector of OP, intersecting OP at Q.
(iii) Taking Q as centre and OQ = PQ as radius, draw a circle to intersect the given circle at T and T'.
(iv) Join PT and PT' to get the required tangents as PT and PT'.
संबंधित प्रश्न
Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other an angle of 60º.
Draw a circle of radius 4.5 cm. Draw two tangents to this circle so that the angle between the tangents is 60°.
Draw a circle of radius 32 cm. Draw a tangent to the circle making an angle 30° with a line passing through the centre.
Use ruler and compass only for answering this question.
Draw a circle of radius 4 cm. Mark the centre as O. Mark a point P outside the circle at a distance of 7 cm from the centre. Construct two tangents to the circle from the external point P.
Measure and write down the length of any one tangent.
Draw a circle with centre O and radius 3 cm. Take a point P outside the circle. Draw tangents to the circle from P without using the centre and using only ruler and compasses.
Using ruler and compasses only, draw tangents to a circle of radius 3 cm from a point 5 cm from the centre. What is the length of each of them ?
Draw two circles of radii 3.5 cm and 2 cm respectively so that their centres are 6 cm apart. Draw direct common tangents to the circle and show that they are equal in length.
Draw a circle at a radius of 3 cm. Take a point at 5.5 cm from the center at the circle. From point P, draw two tangents to the circle.
Draw a circle of radius 4 cm. Take a point P outside the circle without using the center at the circle. Draw two tangents to the circle from point P.
A pair of tangents can be constructed to a circle inclined at an angle of 170°.
