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Quantitative Aptitude
Geometry
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NTPC Graduate Tier 1 2025 Shift-3 📅 05 Jun, 2025

In a circle, the length of a chord is 12 cm and the perpendicular distance from the centre of the circle to the chord is 5 cm. What is the radius of the circle? (Rounded up to two decimal places.)

A
7.81 cm
B
6.97 cm
C
9.87 cm
D
10.25 cm
Result Summary
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NTPC Graduate Tier 1
2025 • 05 Jun, 2025 • Shift-3
In a circle, the length of a chord is 12 cm and the perpendicular distance from the centre of the circle to the chord is 5 cm. What is the radius of the circle? (Rounded up to two decimal places.)
Correct Answer
7.81 cm
[Geometric Theorem Application]: A foundational property of circle geometry states that a perpendicular dropped from the exact center of a circle to any chord b......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Quantitative Aptitude
Chapter -
Ref. Topic Geometry
Pg. No -
💡 Analysis & Explanation
[Geometric Theorem Application] ▼
A foundational property of circle geometry states that a perpendicular dropped from the exact center of a circle to any chord bisects (cuts perfectly in half) that specific chord.
[Right Triangle Construction] ▼
By drawing a line from the center to the edge of the chord, we form a right-angled triangle. The radius (r) becomes the hypotenuse. The perpendicular distance (5 cm) is one leg. The bisected half-chord (12 / 2 = 6 cm) acts as the baseline leg.
[Pythagorean Calculation] ▼
We apply Pythagoras' theorem: Hypotenuse² = Base² + Perpendicular². Substituting the numbers: r² = 6² + 5² = 36 + 25 = 61.
[Final Root Extraction] ▼
To find 'r', we must extract the square root of 61. Since 61 lies between 49 (7²) and 64 (8²), the root is between 7 and 8. The precise calculation gives approximately 7.8102...
Conclusion ▼
Rounded to two decimals, the radius is 7.81 cm.
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