Given: Two concentric circles with AB tangent to smaller circle at R Prove: AR=RB
2 answers:
Answer:
See explanation
Step-by-step explanation:
If segment AB is tangent to the smaller circle, than AB⊥OR. Consider two right triangles AOR and BOR. In these triangles:
- OR is common leg;
- AO=OB as radii of larger circle;
- ∠ARO=∠BRO, because AB⊥OR.
By HL theorem, ttriangles AOR and BOR are congruent. This gives you that AR=RB.
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