Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Steps of construction:
(i) Draw a line OP= 6 cm.
(ii) At O, draw a circle of radius 3.5 cm.
(iii) At P, draw a circle of radius 2 cm.
(iv) At O, draw a third circle concentric to the bigger circle and radius = (3.5 - 2) cm= 1.5 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 circles intersect each other.
(vii) Join OT and OS and extend lines to meet the bigger cirde at A and B.
(viii) Join PT and PS.
(ix) On PT and PS, draw perpendiculars to meet the smaller circle at Mand N.
(x) Join AM and BN.
AM and BN are the required tangents.
Proof:
Since AT || PM and BS || PN; therefore AM = PT and BN = PS
Now in Δ OTP and Δ OSP
PT = PS (Tangents to a circle from same point)
Therefore, AM = BN
Hence, proved.
APPEARS IN
संबंधित प्रश्न
Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60° to each other.
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 given figure, PQ is a tangent to the circle at A. AB and AD are bisectors of ∠CAQ and ∠PAC. if ∠BAQ = 30°. Prove that:
- BD is a diameter of the circle.
- ABC is an isosceles triangle.
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.
Construct an equilateral triangle ABC with side 6 cm. Draw a circle circumscribing the triangle ABC.
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.
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 ______.
