Build equations from touching circles, then use the stated region to choose the circle that fits.
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First lesson in this subject: Complete the angle sum
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A radius meets a tangent line at a right angle. A circle inside a right triangle therefore has its center r from each perpendicular side. Tangent segments from the same corner have equal lengths.
For legs 6 and 8, Pythagoras gives the hypotenuse 10. If the remaining tangent lengths are x and y, then 6 = r + x, 8 = r + y and 10 = x + y. Subtract to get 6 + 8 − 10 = 2r, so r = 2. This derives r = (a + b − c)/2, rather than guessing from the picture.
You are reading the opening. Members read every lesson and guide in full. A free account reads the first lesson in each subject in full.
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First lesson in this subject: Complete the angle sum
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Practice · Use tangent lines, circle centers and labeled measurements to find the radius that fits.
Book · Explore measurements, transformations, coordinates and geometric relationships through diagrams and worked examples.
Previous lesson · Turn circle tangency into distances between centers, then use a right triangle to find a radius.
Next lesson · Identify opposite, adjacent and hypotenuse before using sine, cosine or tangent.
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