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 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?
एक वृत्त जिसका केंद्र O है, उसमें दो जीवा (chords) AB और CD एक-दूसरे को समकोण (right angle) पर काटती हैं। यदि केंद्र O से जीवा AB की दूरी 3 सेमी है तथा केंद्र O से जीवा CD की दूरी 4 सेमी है, तो वृत्त की त्रिज्या क्या होगी?
Detailed Solution & Logic
5 cm / 5 सेमी
दी गई जानकारी:
- दो जीवा AB और CD एक-दूसरे को समकोण (90°) पर काटती हैं
- O से AB की दूरी = 3 cm
- O से CD की दूरी = 4 cm
Concept:
जब दो जीवा एक-दूसरे को समकोण पर काटती हैं, तो केंद्र से उन पर खींची गई लंब दूरी (perpendicular distances) के वर्गों का योग, त्रिज्या के वर्ग के बराबर होता है।
$ r^2 = d_1^2 + d_2^2 $
अब मान रखते हैं:
$ r^2 = 3^2 + 4^2 = 9 + 16 = 25 $
$ r = \sqrt{25} = 5 $
अंतिम उत्तर: 5 cm ✅
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