Contradiction proof. Tangent to a circle w/ radius meeting tanget. Prove radius is shorter than another line (from center, not radius) connecting w/ tangent. Complete proof please.

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Contradiction proof. Tangent to a circle w/ radius meeting tanget. Prove radius is shorter than another line (from center, not radius) connecting w/ tangent. Complete proof please.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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I tried. I couldn't find anything.
Why a contradiction? Can't you use the fact that the hypotenuse of a right triangle is longer than the legs for a direct proof?
Idk, it says contradiction. But the gist of the question is do you absolutely need to use the tangent is perp to radius thm?

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