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प्रश्न
How many common tangents can be drawn to two circles which touch each other internally?
(A) One (B) Two (C) Three (D) Four
उत्तर
(1) A
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संबंधित प्रश्न
If two circles with radii 8 cm and 3 cm respectively touch externally, then find the distance between their centres.
Two circles having radii 3.5 cm and 4.8 cm touch each other internally. Find the distance between their centres.
Four alternative answers for the following question is given. Choose the correct alternative.
Two circles of radii 5.5 cm and 4.2 cm touch each other externally. Find the distance between their centres
If radii of two circles are 4 cm and 2.8 cm. Draw a figure of this circles touching each other externally.
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(2) ∆APR ~ ∆RQB, and
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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 ?
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Line l touches a circle with centre O at point P. If radius of the circle is 9 cm, answer the following.
- What is d(O, P) = ? Why?
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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
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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`]
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