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Math Help - Finding the angle between tangents

  1. #1
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    Finding the angle between tangents

    Verify that the circles x2+y2 = 25 and (x−5)2+(y−10)2= 50 intersect at A = (4, 3).


    Find the size of the acute angle formed at A by the intersecting circles. You will first have to decide what is meant by the phrase the angle formed by the intersecting circles
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  2. #2
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    Re: Finding the angle between tangents

    Hey romean2015.

    Hint: Substitute either x^2 or y^2 into the other equation to get a quadratic in terms of one variable and solve.
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    Re: Finding the angle between tangents

    Angle formed by two curves is the angle between the tangents to the curves at the point of intersection. First find the point of intersection and then the slopes of tangents and proceed further. Angle between two lines with slopes m and n is given by (m-n)/(1+mn)
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  4. #4
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    Re: Finding the angle between tangents

    Point A lies on both circles.Angle between the tangents @A is found by finding the slopes of each line.First slope =-1/7 and second is -4/3.Proceed to find the angle between them
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    Re: Finding the angle between tangents

    If α is the angle between the tangents then tanα= (m_1- m_2)/(1+ m_1 m_2 )
    Thus we have tanα= (-4/3-( - 1/7))/(1+( -4/3)(-1/7)) , Now simplify further and find α;
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  6. #6
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    Re: Finding the angle between tangents

    an easier method
    angle between tangents
    90 -(arctan4/3 +arctan1/7) =45degrees
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