Advertisements
Advertisements
प्रश्न
Draw circles with centres A, B and C each of radius 3 cm, such that each circle touches the other two circles.
उत्तर
Radius of each circle = 3 cm
If two circles touch each other externally, then the distance between their centres is equal to the sum of their radii.
∴ AB = 3 cm + 3 cm = 6 cm
BC = 3 cm + 3 cm = 6 cm
CA = 3 cm + 3 cm = 6 cm
Draw a line seg AB = 6 cm.
With A as centre and radius = 6 cm, mark an arc.
With B as centre and radius = 6 cm, mark an arc intersecting the previous drawn arc at C.
Join AC and BC.
Now, with A, B and C as centres and radius = 3 cm, draw three circles.
It can be seen that, each circle touches the other two circles.
APPEARS IN
संबंधित प्रश्न
If two circles with radii 5 cm and 3 cm respectively touch internally, find the distance between their centres.
If two circles with radii 8 cm and 3 cm, respectively, touch internally, then find the distance between their centers.
In the given figure, the circles with centres P and Q touch each other at R. A line passing through R meets the circles at A and B respectively. Prove that – (1) seg AP || seg BQ,
(2) ∆APR ~ ∆RQB, and
(3) Find ∠ RQB if ∠ PAR = 35°
In the given figure, ray PQ touches the circle at point Q. PQ = 12, PR = 8, find PS and RS.
Four alternative answers for the following question is given. Choose the correct alternative.
Two circles of radii 5.5 cm and 3.3 cm respectively touch each other. What is the distance between their centers ?
Four alternative answers for the following question is given. Choose the correct alternative.
Two circles intersect each other such that each circle passes through the centre of the other. If the distance between their centres is 12, what is the radius of each circle?
Four alternative answers for the following question is given. Choose the correct alternative.
A circle touches all sides of a parallelogram. So the parallelogram must be a, ______
Four alternative answers for the following question is given. Choose the correct alternative.
Chords AB and CD of a circle intersect inside the circle at point E. If AE = 5.6, EB = 10, CE = 8, find ED.
In the given figure, circle with centre M touches the circle with centre N at point T. Radius RM touches the smaller circle at S. Radii of circles are 9 cm and 2.5 cm. Find the answers to the following questions hence find the ratio MS:SR.
(1) Find the length of segment MT
(2) Find the length of seg MN
(3) Find the measure of ∠NSM.
In the adjoining figure circles with centres X and Y touch each other at point Z. A secant passing through Z intersects the circles at points A and B respectively. Prove that, radius XA || radius YB. Fill in the blanks and complete the proof.
Construction: Draw segments XZ and YZ.
Proof:
By theorem of touching circles, points X, Z, Y are `square`.
∴ ∠XZA ≅ `square` ...(opposite angles)
Let ∠XZA = ∠BZY = a ...(I)
Now, seg XA ≅ seg XZ ...[Radii of the same circle]
∴∠XAZ = `square` = a ...[isosceles triangle theorem](II)
Similarly,
seg YB ≅ seg YZ ...[Radii of the same circle]
∴∠BZY = `square` = a ...[isosceles triangle theorem](III)
∴ from (I), (II), (III),
∠XAZ = `square`
∴ radius XA || radius YZ ...[`square`]
If two circles with diameters 8 cm and 6 cm respectively touch externally, find the distance between their centers.
Two circles of radii 5.5 cm and 3.3 cm respectively touch each other externally. What is the distance between their centres?
Four alternative answers for the following question is given. Choose the correct alternative.
Two circles having diameters 8 cm and 6 cm touch each other internally. Find the distance between their centres.
Line ℓ touches a circle with center O at point P. If the radius of the circle is 9 cm, answer the following.
If d(O, Q) = 8 cm, where does the point Q lie?
Line ℓ touches a circle with centre O at point P. If radius of the circle is 9 cm, answer the following.
If d(O, R) = 15 cm, how many locations of point R are line on line l? At what distance will each of them be from point P?
