How to find the length of the common tangent to two circles?
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Hi there!
Here's the answer:
•°•°•°•°•°<><><<><>><><>°•°•°•°•°
^^^ For External tangent problem, where tangent lies on same side of circle.
STEPS :
1. Draw the segment connecting the centers of two circles and draw the two radii to the point of tangency
2. From the centre of smaller circle, Delaware a segment parallel to the common tangent till it hits the radius of the larger circle (or the extension of the radius in a common internal tangent problem)
3. Now, a Right angled triangle is observed and by applying Pythagorean theorem the problem can be finished. Note the simple fact that the opposite sides of rectangle are congruent.
^^^ The same steps can also be applied for internal tangent problems.
Tip:
***** Note the location of hypotenuse in a common tangent problem, the segment connecting the centres of circles is always the hypotenuse of a right angle.
The common tangent is always side of Rectangle, not hypotenuse.
°°°° In a Common tangent problem, segment connecting the centres of circle is never one side of right angle.
•°•°•°•°•°<><><<><>><><>°•°•°•°•°
Here's the answer:
•°•°•°•°•°<><><<><>><><>°•°•°•°•°
^^^ For External tangent problem, where tangent lies on same side of circle.
STEPS :
1. Draw the segment connecting the centers of two circles and draw the two radii to the point of tangency
2. From the centre of smaller circle, Delaware a segment parallel to the common tangent till it hits the radius of the larger circle (or the extension of the radius in a common internal tangent problem)
3. Now, a Right angled triangle is observed and by applying Pythagorean theorem the problem can be finished. Note the simple fact that the opposite sides of rectangle are congruent.
^^^ The same steps can also be applied for internal tangent problems.
Tip:
***** Note the location of hypotenuse in a common tangent problem, the segment connecting the centres of circles is always the hypotenuse of a right angle.
The common tangent is always side of Rectangle, not hypotenuse.
°°°° In a Common tangent problem, segment connecting the centres of circle is never one side of right angle.
•°•°•°•°•°<><><<><>><><>°•°•°•°•°
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