A triangle ABC has a circle inscribed within it with sides a, b, c. The area of the triangle is A. What is the radius of the inscribed circle?
A triangle ABC has a circle inscribed within it with sides a, b, c. The area of the triangle is A. What is the radius of the inscribed circle?
एक त्रिभुज ABC के भीतरa, b, c भुजाओं वाला एक वृत्त बना हुआ हैं। त्रिभुज का क्षेत्रफल A है, इस वृत्त की त्रिज्या क्या है?
Detailed Solution & Logic
Correct Answer:
$\frac{2A}{a+b+c}$
Given:
त्रिभुज ABC की भुजाएँ = $a, b, c$
क्षेत्रफल = $A$
हमें अंतःवृत्त (incircle) की त्रिज्या (r) निकालनी है।
Step 1: Semi-perimeter (अर्ध परिमाप)
$s = \frac{a + b + c}{2}$
Step 2: Formula (Important Relation)
त्रिभुज का क्षेत्रफल = $A = r \times s$
Step 3: r निकालें
$r = \frac{A}{s}$
Final Answer:
👉 $r = \frac{A}{s} = \frac{2A}{a + b + c}$
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