Question
Download Solution PDFवर्तुळात 75° च्या कोनात एकमेकांकडे झुकलेल्या स्पर्शिकेची जोडी काढण्यासाठी, वर्तुळाच्या त्या दोन त्रिज्यांच्या शेवटच्या बिंदूंवर स्पर्शिका काढणे आवश्यक आहे, ज्याच्या दरम्यानचा कोन आहे:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
त्रिज्या स्पर्शबिंदूवर स्पर्शिकेला लंब असते
चतुर्भुजाच्या सर्व कोनांची बेरीज = 360°
गणना:
PA आणि PB या बाह्य बिंदू P पासून वर्तुळाकडे काढलेल्या स्पर्शिका आहेत.
∠OAP = ∠OBP = 90° (त्रिज्या स्पर्शबिंदूवर स्पर्शिकेला लंब असते)
आता, चतुर्भुज OAPB मध्ये,
∠APB + ∠OAP + ∠AOB + ∠OBP = 360°
75° + 90° + ∠AOB + 90° = 360°
∠AOB = 105°
अशा प्रकारे, दोन त्रिज्या, OA आणि OB मधील कोन 105° आहे.
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