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Common external tangents and common internal tangents are two types of tangents that can be drawn between two circles. Common external tangents touch each circle at one point without intersecting the line segment joining the circles' centers, while common internal tangents intersect this line segment. The key difference lies in their geometric relationship to the circles: external tangents do not pass between the circles, whereas internal tangents do. Each type can be determined based on the relative positions and sizes of the circles involved.

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Although normally it is the line that is considered to be tangent to an arc, an arc can be tangent to infinitely many lines and so the answer to the question is: in infinitely many ways.


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The tangent ratio is defined in several different ways. One of these consists of infinite series: the series for the tangent function contains some coefficients which are difficult to calculate. However, the tangent series van be easily calculated from the sine and cosine ratios.sin(x) = x - x3/3! + x5/5! - x7/7! + ...andcos(x) = 1 - x2/2! + x4/4! - x6/6! + ...where x is the angle defined in radians, and n! represents 1*2*3*...*n.So tan(x) = sin(x)/cos(x).None of these require a right angle.


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If: y = x-4 and y = x2+y2 = 8 then 2x2-8x+8 = 0 and the 3 ways of proof are: 1 Plot the given values on a graph and the line will touch the curve at one point 2 The discriminant of b2-4ac of 2x2-8x+8 must equal 0 3 Solving the equation gives x = 2 or x = 2 meaning the line is tangent to the curve

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