Question
Download Solution PDFΔABC केंद्र O वाले एक वृत्त के अंतर्गत है। यदि AB = 17 सेमी, BC = 10 सेमी और AC = 9 सेमी है, AO की लंबाई ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
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उपयोग की गई संकल्पना:
परित्रिज्या की लंबाई = (A × B × C)/(4 × Δ)
जहां A, B, C त्रिभुज की 3 भुजाओं की लंबाई हैं
Δ → त्रिभुज का क्षेत्रफल
त्रिभुज का क्षेत्रफल = √{s(s - a)(s - b)(s - c)}
जहां a, b, c त्रिभुज की 3 भुजाओं की लंबाई हैं
s → अर्द्धपरिधि
गणना:
s = (a + b + c)/2
⇒ s = (10 + 9 + 17)/2
⇒ s = 18
ΔABC का क्षेत्रफल = √{18(18 - 10)(18 - 9)(18 - 17)
⇒ √(18 × 8 × 9 × 1)
⇒ 36 सेमी2
त्रिभुज की परित्रिज्या = (a × b × c)/4Δ
⇒ (10 × 17 × 9)/(4 × 36)
⇒ 10.6 सेमी
∴ त्रिभुज की परित्रिज्या 10.6 सेमी है।
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