# Finding the angle between tangents

• Feb 6th 2013, 05:39 PM
romean2015
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
• Feb 6th 2013, 06:49 PM
chiro
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.
• Feb 6th 2013, 08:50 PM
ibdutt
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)
• Feb 8th 2013, 12:31 PM
bjhopper
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
• Feb 8th 2013, 08:31 PM
ibdutt
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;
• Feb 9th 2013, 09:05 PM
bjhopper
Re: Finding the angle between tangents
an easier method
angle between tangents
90 -(arctan4/3 +arctan1/7) =45degrees