Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Steps of construction:
(i) Take a point O in the plane paper and draw a circle of radius 3 cm.
(ii) Mark a point P at distance 5.5 cm from the centre O and join OP.
(iii) Draw the right bisector at OP, intersecting OP at Q.
(iv) Taking Q as the centre and OQ = PQ as radius, draw a circle to intersect the given circle at T and T'.
(v) Join PT and PT' to get the required tangent.
Taype (II). Construction of a tangent to a circle from an external point when its centre is known.
Steps of construction:
Let P be the external point from where the tangent are to be drawn to the given circle.
(i) Through P draw a secant PAB to intersect the circle at A and B.
(ii) Join AP to a point C such that AP = DX is equal to the mid-point at AC.
(iii) Draw a semicircle with BC as diameter.
(iv) Draw PD ⊥ BCX intersecting the semicircle at D.
(v) With P as centre and PD as radius draw arcs to intersect the given circle at T and T'.
(vi) Join PT and PT'. Then PT and PT' are the required tangent.
संबंधित प्रश्न
Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Give the justification of the construction.
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.
Draw two circles of radii 3 cm and 3.5 cm, their centres being 8 cm apart. Construct a transverse common tangent and measure its length.
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.
Use a ruler and a pair of compasses to construct ΔABC in which BC = 4.2 cm, ∠ ABC = 60°, and AB 5 cm. Construct a circle of radius 2 cm to touch both the arms of ∠ ABC of Δ ABC.
Draw two lines AB, AC so that ∠ BAC = 40°:
(i) Construct the locus of the center of a circle that touches AB and has a radius of 3.5 cm.
(ii) Construct a circle of radius 35 cm, that touches both AB and AC, and whose center lies within the ∠ BAC.
To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°. It is required to draw tangents at the end points of those two radii of the circle, the angle between which is ______.
To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°. It is required to draw tangents at the end points of those two radii of the circle, the angle between which is ______.
Draw a circle of radius 4 cm. Construct a pair of tangents to it, the angle between which is 60º. Also justify the construction. Measure the distance between the centre of the circle and the point of intersection of tangents.
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.
