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Two circles radii 6cm and 4cm have their centers 8cm apart Construct a direct common tangent and measure its length?
Wiki User
∙ 11y ago
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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).
Wiki User
∙ 11y ago
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What is a tangent intersecting the segment joining the centers of the two circles?
They are the common tangents to the circles.
Define common internal tangent of 2 circles?
it intersects the segment joining the centers of two circles
How do you find an internal tangent of 2 circles?
you draw a triangle formed by the centers of the two circles and use pythagoean theorem
What are tangent circles?
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.
Do tangent circles have the same center?
No, tangent circles do not have the same center. They just touch at the side. Here is an example:
What is a tangent intersecting the segment joining the centers of the two circles?
They are the common tangents to the circles.
Define common internal tangent of 2 circles?
it intersects the segment joining the centers of two circles
How do you find an internal tangent of 2 circles?
you draw a triangle formed by the centers of the two circles and use pythagoean theorem
Are tangent circles two circles that are tangent to the same line at the same point?
Yes.
What are tangent circles?
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.
Do tangent circles have the same center?
No, tangent circles do not have the same center. They just touch at the side. Here is an example:
Can two circles be tangent at the same point?
If the two circles are tangent to each other,then it must be at the same point.
Can a tangent circle be concentric?
No; tangent circles touch each other at one point but concentric circles cannot not touch.
Are circles tangent when they meet at a single point?
Yes, circles that share one and only one point are tangent to each other.
Can a line be tangent to one circle and a secant to the other in concentric circles?
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.
What are two coplanar circles that intersect at exactly one point?
Tangent circles.
A line that is tangent to two circles?
... touches each circle in exactly one point on each circle. given any two circles where none is entirely inside or inside and tangent to the other, there are at most four straight lines that are tangent to both circles.
