Question : The radius of the incircle of a triangle whose sides are 9 cm, 12 cm, and 15 cm is:
Option 1: 9 cm
Option 2: 13 cm
Option 3: 3 cm
Option 4: 6 cm
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Correct Answer: 3 cm
Solution : Checking for the triangle by using Pythagoras theorem. $9^2 + 12^2 = 15^2$ Thus, The triangle is right-angled. Given, AB = 9, BC = 12 cm OD = OE = OF = $x$ cm (radius of the circle) And, BEOD is a square. AD = AF = $9-x$ ($\because $ The length of the tangent from a point to the circle is the same.) EC = CF = $12-x$ ($\because $ The length of the tangent from a point to the circle is the same.) $\therefore$ AC = AF + FC ⇒ $9-x+12-x = 15$ ⇒ $21-2x = 15$ ⇒ $2x = 21-15$ ⇒ $2x = 6$ ⇒ $x = \frac{6}{2} = 3$ Hence, the correct answer is 3 cm.
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