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Two circles have the radii 6 and 3 cm. The distance between their centers is 18cm. Find the length of the common external tangent.
See figure.
Hello reiwardI think the diagram should look like the one I have attached.Originally Posted by reiward
So, in this diagram, the angles at,
and
are all right angles.
cm;
cm;
cm. We need to calculate
, which is the same length as
.
Can you complete it now?
Hint:Spoiler:
Grandad
Hello reiwardI think you'll find that's the common internal tangent.
But if you need its length, draw the line joining the centres of the circles. Then use similar triangles, with one pair of corresponding sides being radii of the two circles. So the tangent crosses the line joining the centres at a point dividing it in the ratio 2:1; the distances from the centres of this point therefore being 12 cm and 6 cm.
Then use Pythagoras on the triangles to find the lengths of the two parts of the tangent. Add together. Answer: 15.59 cm
Grandad
Here comes a slightly different attempt:
1. Draw a circle aroundwith radius
.
2. Draw the tangent fromto the new, greater circle. (Red line).
3. This red line segment is parallel to the internal tangent and has the same length as the internal tangent.
4. The indicated triangle is a right triangle with hypotenuseand one leg
. Use Pythagorean theorem to calculate the length of the internal tangent..
5. With your example:
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