Question

Complete the proof.
Given:
R↔S tangent to circle A and circle B at points R and S.
Prove:
AR ∥ BS

Answer 1

The proof is shown below:

What is tangent?

The tangent is defined as a line touching circles or an ellipse at only one point.

As, tangent line is perpendicular to radius of the circle.

So,

AR ⊥ RS

BS ⊥ RS

Thus, AR and BS ⊥ to same line RS.

Now, either AR or BS are in same line or parallel.

since, they are the radius of different circles.

Hence, AR ║BS.

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