SBI Clerk Prelims practice question
A right-angled triangle has legs of length 7 cm and 24 cm, and hypotenuse 25 cm. A circle is inscribed in the triangle, touching all three sides. Find the length of the tangent segment from the vertex opposite the side of length 24 cm to its point of contact with the incircle.
From a SBI Clerk Prelims Quantitative Aptitude practice set · Quantitative Aptitude
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Correct answer: (A) 21 cm
Semi-perimeter s = (7+24+25)/2 = 28. For a triangle with an inscribed circle, the tangent length from each vertex equals s minus the side opposite that vertex. The vertex opposite the side of length 24 cm has tangent length = s − 24 = 28 − 24 = 21 cm.
हिंदी में प्रश्न
एक समकोण त्रिभुज की भुजाएँ 7 सेमी और 24 सेमी तथा कर्ण 25 सेमी है। त्रिभुज में एक वृत्त अंतर्निहित (इनस्क्राइब्ड) है, जो तीनों भुजाओं को स्पर्श करता है। 24 सेमी लंबाई वाली भुजा के सम्मुख शीर्ष से अंतःवृत्त के साथ उसके स्पर्श बिंदु तक की स्पर्श रेखा खंड की लंबाई ज्ञात कीजिए।
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सही उत्तर: (A) 21 cm
अर्ध-परिमाप s = (7+24+25)/2 = 28। अंतःवृत्त वाले त्रिभुज में, प्रत्येक शीर्ष से स्पर्श रेखा की लंबाई = s − (उस शीर्ष के सम्मुख भुजा) होती है। 24 सेमी लंबाई वाली भुजा के सम्मुख शीर्ष से स्पर्श रेखा की लंबाई = s − 24 = 28 − 24 = 21 सेमी।
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