In a circle, there is a chord measuring 20 cm that is located 15 cm away from the center. what is the approximate radius of the circle?
In a circle, there is a chord measuring 20 cm that is located 15 cm away from the center. what is the approximate radius of the circle?
एक वृत्त में, 20 सेमी माप की एक जीवा है जो केंद्र से 15 सेमी दूर स्थित हैं। वृत्त की अनुमानित त्रिज्या क्या हैं?
Detailed Solution & Logic
Correct Answer:
18 cm
The perpendicular from the center of a circle to a chord bisects the chord.
These form a right-angled triangle with the radius as the hypotenuse.
Length of chord= $ \dfrac{20}{2}=10 $
Distance of chord from the center = 15 cm
Using Pythagoras theorem:
$ r^2=15^2+10^2 $
$ r^2=225+100=325 $
$ r=\sqrt{325} = 18\ \text{cm} $
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