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प्रश्न
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.
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उत्तर
Steps for construction:
- Draw AB = 5 cm using a ruler.
- With A as the centre cut an arc of 3 cm on AB to obtain C.
- With A as the centre and radius 2.5 cm, draw an arc above AB.
- With same radius and C as the centre draw an arc to cut the previous arc and mark the intersection as O.
- With O as the centre and radius 2.5 cm, draw a circle so that points A and C lie on the circle formed.
- Join OB.
- Draw the perpendicular bisector of OB to obtain the mid-point of OB, M.
- With the M as the centre and radius equal to OM, draw a circle to cut the previous circle at points P and Q.
- Join PB and QB. PB and QB are the required tangents to the given circle from exterior point B.
QB = PB = 3 cm
That is, length of the tangents is 3 cm.
संबंधित प्रश्न
In the figure given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find:
1) AB.
2) the length of tangent PT.
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°.
Draw a circle of radius 4.2. Draw a pair of tangents to this circle inclined to each other at an angle of 45°
Construct a tangent to a circle of radius 4 cm form a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.
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 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 two concentric circles with radii 4 cm and 6 cm. Taking a point on the outer circle, construct a pair of tangents to inner circle. By measuring the lengths of both the tangents, show that they are equal to each other.
Draw an isosceles triangle with sides 6 cm, 4 cm, and 6 cm. Construct the incircle of the triangle. Also, write the steps of construction.
Construct a tangent to a circle of radius 4 cm from a point which is at a distance of 6 cm from its centre.
