Finding the angle between tangents

Verify that the circles x^{2}+y^{2} = 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

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.

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)

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

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;

Re: Finding the angle between tangents

an easier method

angle between tangents

90 -(arctan4/3 +arctan1/7) =45degrees