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Difficulty: 1/102024 NMTC 2024 (QII-23)

How many different tangents can be drawn on circle?

Guide / Hint

Hint 1: How many points make up the circumference of a circle?

Hint 2: At any single point on the circle, how many tangent lines can touch that point?

Hint 3: Multiply the number of points by the number of tangents per point to find the total.

Solution

Step 1 (Definition of a Tangent): A tangent to a circle is a straight line that touches the circle at exactly one point.

Step 2 (Number of Points on a Circle): A circle is a continuous closed curve containing infinitely many distinct points along its perimeter.

Step 3 (Tangent at Each Point): At every single point on the circumference of a circle, exactly one unique tangent line can be drawn. Since there are infinitely many points, there are infinitely many different tangents that can be drawn on a circle.

Step 4 (Conclusion): The total number of tangents is infinity.

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    2024 NMTC 2024 QII-23 - Olympiad Math Olympiad Question | Leminno