Advertisements
Advertisements
Question
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.
Advertisements
Solution
Steps of construction of transverse common tangent:
(i) Draw a line OP= 7 cm.
(ii) At O, draw a circle of radius 2. 5 cm.
(iii) At P, draw a circle of radius 4 cm.
(iv) At O, draw a third circle concentric to the smaller circle and radius= (2.5 + 4) cm= 6.5 cm
(v) Draw a perpendicular bisector of OP. Let R be the mid-point of OP.
(vi) With Ras centre and OR as radii, draw a fourth circle. Mark as T and S where the third and fourth cireles intersect each other.
(vii) Join OT and OS to meet the smaller circle at A and B.
(viii)Join PT and PS.
(ix) On PT and PS, draw perpendiculars to meet the bigger circle at Mand N.
(x) Join AM and BN.
AM and BN are the required tangents.
Steps of construction of direct common tangent:
(i) Draw a line OP= 7 cm.
(ii) At O, draw a circle of radius 4 cm.
(iii) At P, draw a circle of radius 2.5 cm.
(iv) At O, draw a third circle concentric to the bigger circle and radius = ( 42.5) cm= 1.5 cm
(v) Draw a perpendicular bisector of OP. Let R be the mid-point of OP.
(vi) With Ras centre and OR as radii, draw a fourth circle. Mark as T and S where the third and fourth cireles intersect each other.
(vii) Join OT and OS and extend lines to meet the bigger cir de at A and B.
(viii) Join PT and PS.
(ix) On PT and PS, draw perpendiculars to meet the smaller circle at M and N.
(x) Join AM and BN.
AM and BN are the required tangents.
On measuring, AM= BN = 7 cm.
APPEARS IN
RELATED QUESTIONS
Draw a circle of radius 3 cm. Draw a pair of tangents to this circle, which are inclined to each other at an angle of 60º.
In the figure given below, O is the centre of the circle and SP is a tangent. If ∠SRT = 65°,
find the value of x, y and z.
Construct an equilateral triangle ABC with side 6 cm. Draw a circle circumscribing the triangle ABC.
Draw a circle of radius of 3 cm. Take two points P and Q on one of its diameters extended on both sides, each at a distance of 7 cm on opposite sides of its centre. Draw tangents to the circle from these two points P and Q ?
Take a point O on the plane at the paper. With O as center draw a circle of radius 3 cm. Take a point P on this circle and draw a tangent at P.
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.
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.
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 2.5 cm. Construct a pair of tangents from a point Pat a distance of 6 cm from the centre of the circle.
Using ruler and compass construct a triangle ABC in which AB = 6 cm, ∠BAC = 120° and AC = 5 cm. Construct a circle passing through A, B and C. Measure and write down the radius of the circle.
