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Suppose A and B are the centres of the larger and smaller circles respectively. Suppose that the tangent to circle A is at D and the tangent to circle B is at C.
Consider the quadrilateral ABCD.
AD = 6 cm, BC = 4 cm and AB = 8 cm.
Also angles ADC and DCB are right angles so that AD CB.
Thus ABCD is a right angled trapezium.
Draw a perpendicular from B onto AD to meet it at E. Then BCDE is a rectangle, and ABE is a right angled triangle.
EA = DA - DE = DA - CB = 6 - 4 = 2
and
EB = CD (opp sides of a rectangle),
So, in ABE, AB2 = AE2 + EB2
82 = 22 + EB2
64 = 4 + CD2
So CD = sqrt(60) = 2*sqrt(15) cm = 7.746 cm (approx).
To construct a Pappus chain within an arbelos, begin by identifying the three semicircles that define the arbelos, which are formed by three tangent circles. From the points where these semicircles touch, draw circles tangent to each other and to the sides of the arbelos. The centers of these tangent circles will form a chain, known as the Pappus chain, which can be extended infinitely. This construction utilizes the unique properties of the arbelos and the relationships of tangency among the circles.
They are the common tangents to the circles.
it intersects the segment joining the centers of two circles
you draw a triangle formed by the centers of the two circles and use pythagoean theorem
Tangent circles are circles that touch one another without crossing. The distance between the centres of the circles must be equal to the difference or the sum of their radii.
To construct a Pappus chain within an arbelos, begin by identifying the three semicircles that define the arbelos, which are formed by three tangent circles. From the points where these semicircles touch, draw circles tangent to each other and to the sides of the arbelos. The centers of these tangent circles will form a chain, known as the Pappus chain, which can be extended infinitely. This construction utilizes the unique properties of the arbelos and the relationships of tangency among the circles.
They are the common tangents to the circles.
it intersects the segment joining the centers of two circles
you draw a triangle formed by the centers of the two circles and use pythagoean theorem
Yes.
Tangent circles are circles that touch one another without crossing. The distance between the centres of the circles must be equal to the difference or the sum of their radii.
No, tangent circles do not have the same center. They just touch at the side. Here is an example:
If the two circles are tangent to each other,then it must be at the same point.
No; tangent circles touch each other at one point but concentric circles cannot not touch.
Yes, the measure of a tangent-chord angle is indeed twice the measure of the intercepted arc. This is a key property of circles in geometry. Specifically, if a tangent and a chord intersect at a point on the circle, the angle formed between them is equal to half the measure of the arc that lies between the points where the chord intersects the circle.
Yes, circles that share one and only one point are tangent to each other.
Yes, it can as long as it is not the tangent line of the outermost circle. If it is tangent to any of the inner circles it will always cross the outer circles at two points--so it is their secant line--whereas the tangent of the outermost circle is secant to no circle because there are no more circles beyond that last one.