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Circles
RD Sharma
CBSE
Grade 10

Question:

A circle is inscribed in a $\Delta ABC$ touching $AB, BC, CA$ at $P, Q, R$ respectively. If $AB = 10\text{ cm}, BC = 12\text{ cm}, CA = 8\text{ cm}$, find $AP, BQ, CR$.

Step-by-Step Solution

Key Concept: Let $AP = AR = x, BP = BQ = y, CQ = CR = z$. $x + y = 10, y + z = 12, z + x = 8$. Sum $= 2(x+y+z) = 30 \Rightarrow x+y+z = 15$. $x = 15-12 = 3, y = 15-8 = 7, z = 15-10 = 5$. $AP = 3\text{ cm}, BQ = 7\text{ cm}, CR = 5\text{ cm}$.
$x + y + z = 15$. [0.5 Mark]
$x = 15 - 12 = 3\text{ cm}$, $y = 15 - 8 = 7\text{ cm}$, $z = 15 - 10 = 5\text{ cm}$. [1.5 Marks]

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🎯 Official CBSE Marking Scheme:
Setting perimeter sum $x+y+z = 15$: 0.5 Mark
Evaluating $AP = 3\text{ cm}, BQ = 7\text{ cm}, CR = 5\text{ cm}$: 1.5 Marks

Correct Answer:
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