Difficulty: Easy
Correct Answer: 10.2 cm
Explanation:
Introduction / Context:
This question checks a very simple but important fact about circles: the largest possible chord is the diameter. Recognizing this allows you to immediately find the radius from the length of the largest chord.
Given Data / Assumptions:
Concept / Approach:
In any circle, the diameter is the longest chord. Every other chord has a length strictly less than the diameter. Therefore, if the problem states that the largest chord has length 20.4 cm, this length must equal the diameter of the circle. The radius is half the diameter:
Radius = Diameter / 2
Step-by-Step Solution:
Step 1: Identify that the largest chord of a circle is its diameter.
Step 2: Given largest chord length is 20.4 cm, so Diameter D = 20.4 cm.
Step 3: Radius r = D / 2.
Step 4: Compute r = 20.4 / 2 = 10.2 cm.
Verification / Alternative check:
Any chord that is not a diameter lies strictly inside the circle and must be shorter than 20.4 cm. Therefore, there is no ambiguity: a circle with radius 10.2 cm has diameter 20.4 cm, and this chord is indeed the largest possible chord.
Why Other Options Are Wrong:
Greater than 10.2 cm or greater than or equal to 10.2 cm: These suggest the radius could be larger than 10.2 cm while still having a largest chord of 20.4 cm, which is impossible because then the diameter would exceed 20.4 cm, contradicting the statement that 20.4 cm is the largest chord.
Less than 10.2 cm: This would give a diameter less than 20.4 cm, so 20.4 cm could not be a chord in that circle at all.
Cannot be determined: The information given is sufficient, because largest chord directly identifies the diameter, so the radius is uniquely determined.
Common Pitfalls:
Sometimes, students overcomplicate such problems by thinking about other chords or by not recalling that the diameter is always the longest chord. Keeping this basic property in mind allows for a quick and accurate solution.
Final Answer:
The radius of the circle is 10.2 cm.
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