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.
Answer:
R is the mid point of AB so AR = RB
Step-by-step explanation:
Points to remember
The diameter of a circle and a chord is mutually perpendicular then the diameter divide the chord in two equal parts.
<u>To prove AR = RB</u>
From the figure we get, AB is the tangent at R of small circle.
Therefore OR ⊥ AB
O is the center of both circles.
AB is the chord of large circle.
So The diameter of large circle passing through R is perpendicular to AB
Therefore AR = RB
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