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प्रश्न
Draw a circle of radius 3 cm. Mark a point P at a distance of 5 cm from the centre of the circle drawn. Draw two tangents PA and PB to the given circle and measure the length of each tangent.
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उत्तर
Steps of construction:
- Draw a circle with centre O and radius 3 cm.
- From O, take a point P such that OP = 5 cm.
- Draw a bisector of OP which intersects OP at M.
- With centre M, and radius OM, draw a circle which intersects the given circle at A and B.
- Join AP and BP.
AP and BP are the required tangents.
On measuring AP = BP = 4 cm.
संबंधित प्रश्न
Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q. Give the justification of the construction.
Draw a line AB = 5 cm. Mark a point C on AB such that AC = 3 cm. Using a ruler and a compass only, construct:
- A circle of radius 2.5 cm, passing through A and C.
- Construct two tangents to the circle from the external point B. Measure and record the length of the tangents.
Draw a circle of diameter 9 cm. Mark a point at a distance of 7.5 cm from the centre of the circle. Draw tangents to the given circle from this exterior point. Measure the length of each tangent.
Using ruler and compasses only, draw an equilateral triangle of side 4.5 cm and draw its circumscribed circle. Measure the radius of the circle.
Draw a circle of radius 4.5 cm. Draw two tangents to this circle so that the angle between the tangents is 60°.
The bisectors of angles A and B of a scalene triangle ABC meet at O.
- What is the point O called?
- OR and OQ are drawn perpendicular to AB and CA respectively. What is the relation between OR and OQ?
- What is the relation between angle ACO and angle BCO?
Draw a pair of tangents to a circle of radius 3 cm, which are inclined to each other at an angle of 60°.
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 two circles with radii 2.5 cm and 4 cm and with their centres 7 cm apart.
Draw a direct common tangent and a transverse common tangent. Calculate the length of the direct common tangent.
Construct a pair of tangents to a circle of radius 4 cm from a point P lying outside the circle at a distance of 6 cm from the centre.
