Solving for the Radius of the Smallest Circle in Three Circles and a Tangent

Three circles with a common tangent are depicted, and the radii of the larger circles are provided in the diagram. By using geometric properties and calculations, the value of the radius of the smallest circle can be determined accurately.

• Geometry
• Circles
• Tangent
• Radius Calculation
• Math

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1. Three Circles and a Tangent

2. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ??? ?? (Not to scale) ? What is the value of the radius of the smallest circle, ??

3. Three Circles and a Tangent ? ? + ? ? ? ? ?

4. Three Circles and a Tangent ? ? ? + ? ? ?

5. Three Circles and a Tangent ? + ? ? ? ? ? ?

6. Three Circles and a Tangent ? + ? ? ? ? ? ? + ? ? + ? ? ?

7. Three Circles and a Tangent ? + ? ? ? ? + ?? ? ??= ? ?? ? ?? = ? ?? + ? ?? ? ? ? + ? ? + ? ? ? ? ?? ? ??

8. Three Circles and a Tangent ? ?? = ? ?? + ? ??

9. Three Circles and a Tangent ? ?? = ? ?? + ? ?? ?? = ?? + ?? ??? both sides 1 1 1 ?= ?+ ? Returning to our problem: 1 1 144+ 1 16 ?= 1 1 12+1 4=1 ?= 3 ? = 9

10. Three Circles and a Tangent 1 1 1 ?= ?+ ? ? ? ?

12. ??? ?? ?

13. RESOURCES

14. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ??? ?? (Not to scale) ? What is the value of the radius of the smallest circle, ??

15. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ???? ??.?? (Not to scale) ? What is the value of the radius of the smallest circle, ??

16. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ???.?? ??.?? (Not to scale) ? What is the value of the radius of the smallest circle, ??

17. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ??? ??.?? (Not to scale) ? What is the value of the radius of the smallest circle, ??

18. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ???.???? ??.?? (Not to scale) ? What is the value of the radius of the smallest circle, ??

19. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ???.?? ??.?? (Not to scale) ? What is the value of the radius of the smallest circle, ??

20. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ???.?? ??.???? (Not to scale) ? What is the value of the radius of the smallest circle, ??

21. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ??.?? ?? (Not to scale) ? What is the value of the radius of the smallest circle, ??

22. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ??.?? ??.?? (Not to scale) ? What is the value of the radius of the smallest circle, ??

23. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ?? ??.???? (Not to scale) ? What is the value of the radius of the smallest circle, ??

24. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ?? ??.?? (Not to scale) ? What is the value of the radius of the smallest circle, ??

25. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ?? ??.?? (Not to scale) ? What is the value of the radius of the smallest circle, ??

26. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ??? ??.?? (Not to scale) ? What is the value of the radius of the smallest circle, ??

27. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ??? ??.???? (Not to scale) ? What is the value of the radius of the smallest circle, ??

28. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ??? ??.?? (Not to scale) ? What is the value of the radius of the smallest circle, ??

29. SIC_48 Three Circles and a Tangent The three circles are touching and share a common tangent. The radii of the two larger circles are as stated in the diagram - all units are cm. ???? ??.???? (Not to scale) ? What is the value of the radius of the smallest circle, ??