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Prove that, "If two circles touch each o...

Prove that, "If two circles touch each other externally, their centres and the point of contact are collinear".

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In the given figure, two circles touch each other externally at the point C. Prove that the common tangent to the circle at C bisects the common tangents at P and Q.

Two circles touch each other externally. Sum of their areas is 90pi cm^2 and the distance between their centres is 12cm. Find their radii.

Knowledge Check

  • Two circle touch each other internally.The distance between their centres is 1.5 cm.IF the radius of one circle is 3.5 cm,then the radius of the other circle is:

    A
    5 cm
    B
    4 cm
    C
    3cm
    D
    2.5 cm

  • If a circle with the point (-1, 1) as the centre touches the line x + 2y + 9 = 0, then the co-ordinates of the point of contact are:

    A
    (-3,3)
    B
    (-3,-3)
    C
    (0,0)
    D
    `(7/3,17/3)`

  • Two circles of radii 4 cm and 3cm touch each other then the distance between their centres will be:

    A
    7cm
    B
    1cm
    C
    Either 7cm or 1cm
    D
    0cm

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    Three circles touch each other externally.Find the radii of the circles if the sides of the triangle formed by joining the centres are 7cm,8cm and 9cm respectively.

    Two circles of radius 25 cm and 9 cm touch each other externally. Find the length of the direct common tangent.

    PQR is a triangle with PQ=10cm, QR=8cm and PR=11cm . Three circles are drawn touching with each other such that the vertices as their centres. Find the radii of each circle.

    Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

    If a circle, whose centre is (-1,1) touches the straight line x+2y = 12, then the co-ordinates of the point of contact are

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