Geometry and TrigonometryHardRadius from a chord and its distance from the centre
Geometry and Trigonometry practice question
A chord of a circle has length 24 and is 5 units from the centre of the circle. What is the radius of the circle?
- A. 13Correct
- B. 12
- C. 17
- D. 24
Answer: A. 13
The perpendicular from the centre bisects the chord, forming a right triangle with legs 5 and 12 and the radius as hypotenuse: √(25 + 144) = 13.
Why the other answers are wrong
- B. 12
- 12 is half the chord, one leg of the triangle.
- C. 17
- 17 adds the legs (5 + 12) instead of using the Pythagorean theorem.
- D. 24
- 24 is the whole chord; the radius is the hypotenuse of a 5-12 right triangle, 13.
More Geometry and Trigonometry questions
- Hard
In a right triangle, one leg is 5 and the hypotenuse is 13. What is the length of the other leg? - Hard
A circle has a radius of 4. What is the length of an arc that subtends a central angle of 90°? - Hard
A circle is defined by the equation (x − 3)² + (y + 2)² = 25. What is the radius of the circle? - Hard
What is 135° expressed in radians? - Hard
What is the length of segment PT? - Hard
What is the measure, in degrees, of the central angle of this sector?
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