Question

Given: Two concentric circles with AB tangent to smaller circle at R Prove: AR=RB

Answer 1

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 2

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.

To prove AR = RB

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