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Prove that the tangent at any point of c...

Prove that the tangent at any point of circle is perpendicular to the radius through the point of contact.

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The correct Answer is:
r =2 cm
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Theorem 10.1 : The tangent at any point of a circle is perpendicular to the radius through the point of contact.

Theorem: A tangent to a circle is perpendicular to the radius through the point of contact.

Knowledge Check

  • Assertion(A) At a point P of a circle with centre O and radius 12cm , a tangent PQ of length 16cm is drawn. Then, OQ=20cm . Reason (R ) The tangent at any point of a circle is perpendicular to the radius through the point of contact.

    A
    Both Assertion (A) and Reason (R ) are true and Reason (R ) is a correct explanation of Asseration (A).
    B
    Both Assertion (A) and Reason (R ) are true but Reason (R ) is not a correct explanation of Asseration (A).
    C
    Assertion(A) is true and Reason (R ) is false.
    D
    Assertion(A) is false and Reason (R ) is true.

  • A tangent at any point of a circle is perpendicular to the radius through the _____.

    A
    chord
    B
    diameter
    C
    point of contact
    D
    all of the above

  • The tangent at any point of the circle is _______to the radius through the point of contact.

    A
    A)parallel
    B
    B)Intersecting
    C
    C)perpendicular
    D
    D)equal

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    The tangent at any point of a circle is ............ to the radius through the point of contact.

    A Tangent to a circle is perpendicular is perpendicular to the radius through the point of contact.

    The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact.Also curve passes through the point (1,1). Then the length of intercept of the curve on the x-axis is

    The perpendicular from the origin to the tangent at any point on a curve is equal to the abscissa of the point of contact. Find the equation of the curve satisfying the above condition and which passes through (1, 1).

    Fill in the blanks: The common point of a tangent and the circle is called...... A circle may have ..... parallel tangents. A tangent to a circle intersects it in ..... point(s). A line intersecting a circle in two points is called a ........ (v) The angle between tangent at a point on a circle and the radius through the point is .........

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