A chord of length 24 cm subtends a right angle at the center of the circle. What is the radius of the circle?
A chord of length 24 cm subtends a right angle at the center of the circle. What is the radius of the circle?
24 सेमी लंबी एक जीवा वृत्त के केंद्र पर समकोण बनाती हैं। वृत्त की त्रिज्या क्या है?
Detailed Solution & Logic
Correct Answer:
\(12\sqrt{2}\)cm/ \(12\sqrt{2}\)सेमी
Solution:
Let the radius be r.
The chord subtends a right angle ($90^\circ$) at the center.
Formula for chord length:
Chord $= 2r \sin\left(\frac{\theta}{2}\right)$
Here $\theta = 90^\circ$, so
Chord $= 2r \sin 45^\circ$
$24 = 2r \times \frac{\sqrt{2}}{2}$
$24 = r\sqrt{2}$
$r = \frac{24}{\sqrt{2}} = 12\sqrt{2}$ cm
Answer: The radius is $12\sqrt{2}$ cm.
Similar Practice Questions
If the total surface area of a hemisphere is \(462\text{cm}^2\) , calculate its radius.
If the total surface area of a hemisphere is \(462\text{cm}^2\) , calculate its radius. यदि...
A cuboid of dimensions 18 cm × 12 cm × 8 cm is melted and recast into smaller cubes each having an edge of 4 cm.
A cuboid of dimensions 18 cm × 12 cm × 8 cm is melted and...
In a circle with center O, two chords, AB and CD, cross each other at right angles. If the distance from the center O to chord AB is 3 cm, while the distance from O to chord CD is 4 cm. What is the radius of the circle?
In a circle with center O, two chords, AB and CD, cross each other at...
Two circles have radii of 8 cm and 3 cm. The distance between their centers is 15 cm. What is the length of a direct common tangent?
Two circles have radii of 8 cm and 3 cm. The distance between their centers...
A regular polygon has interior angle $ 160^\circ $.How many sides does it have?
A regular polygon has interior angle $ 160^\circ $.How many sides does it have? एक...
In a circle, angle subtended by chord AB at the center is $ 80^\circ$. What is the measure of angle $\angle $ACB, Where C lies on the circle?
In a circle, angle subtended by chord AB at the center is $ 80^\circ$. What...
What is the area of a triangle with a base of 12 cm and a height of 8 cm?
What is the area of a triangle with a base of 12 cm and a...