Question:
A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle?
A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle?
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In problems involving tangent circles, use the Pythagorean theorem in combination with geometric properties to solve for unknown radii.
Updated On: Aug 1, 2025
- \( 3 - 2\sqrt{2} \)
- \( 4 - 2\sqrt{2} \)
- \( 7 - 4\sqrt{2} \)
- \( 6 - 4\sqrt{2} \)
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The Correct Option is A
Solution and Explanation
By applying geometry and using the Pythagorean theorem in the right triangle formed by the centers and radii of the two circles, the radius of the smaller circle is found to be \( 3 - 2\sqrt{2} \).
\[
\boxed{3 - 2\sqrt{2}}
\]
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