Advertisements
Advertisements
Question
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.
Advertisements
Solution
Steps of construction:
(i) Draw a line OP= 8 cm.
(ii) At O, draw a circle of radius 3 cm.
(iii) At P, draw a circle of radius 3.5 cm.
(iv) At O, draw a third circle concentric to the smaller circle and radius= (3.5 + 3) cm= 6.5 cm
(v) Draw a perpendicular bisector of OP. Let R be the mid-point of OP.
(vi) With R as centre and OR as radii, draw a fourth circle. Mark as T and S where the third and fourth ci rel es 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 M and N.
(x) Join AM and BN.
AM and BN are the required tangents.
On measuring, AM= BN = 8 cm.
APPEARS IN
RELATED QUESTIONS
Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also measure its length.
Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circles. Give the justification of the construction.
Draw an inscribing circle of a regular hexagon of side 5.8 cm.
Draw a circle of radius 3 cm. Form a point P, 7 cm away from the centre of the circle, draw two tangents to the circle. Also, measure the lengths of the tangents.
Draw a circle of radius 3.5 cm. Take two points A and B on one of its extended diameter, each at a distance of 5 cm from its center. Draw tangents to the circle from each of these points A and B.
Write the steps of construction for drawing a pair of tangents to a circle of radius 3 cm , which are inclined to each other at an angle of 60° .
Draw a circle of radius 4 cm. From a point 6 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.
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 two concentric circles of radii 3 cm and 5 cm. Taking a point on outer circle construct the pair of tangents to the other. Measure the length of a tangent and verify it by actual calculation.
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.
