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Difficulty: 2/102023 NMTC 2023 (QII-31)

The distance between two parallel tangents of circle of radius 6 cm is ________.

Guide / Hint

Hint 1: Recall that parallel tangents touch the circle at opposite endpoints of a diameter.

Hint 2: The perpendicular distance between these parallel lines is equal to the diameter of the circle.

Hint 3: Multiply the radius (6 cm) by 2.

Solution

Step 1 (Tangents and Diameter relation): Two parallel tangents to a circle must touch the circle at the endpoints of a unique diameter.

Step 2 (Calculate the Distance): The distance between two parallel lines tangent to a circle is equal to the length of the diameter of the circle:

We are given the radius is cm:

Step 3 (Conclusion): The distance between the two parallel tangents is exactly 12 cm.

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