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Abc is a Right Triangle in Which ∠B = 90°. If Ab = 8 Cm and Bc = 6 Cm, Find the Diameter of the Circle Inscribed in the Triangle. - Mathematics

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Sum

ABC is a right triangle in which ∠B = 90°.  If AB = 8 cm and BC = 6 cm, find the diameter of the circle inscribed in the triangle.

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Solution

We have given that a circle is inscribed in a triangle

Using pythagoras theorem

`(AC)^2 = (AB)^2 + (BC)^2`

`(AC)^2 = (8)^2 + (6)^2`

`(AC)^2 = 64 + 36`

`(AC)^2 = 100`

⇒ AC = 10

Area of Δ ABC = area of Δ APB + area of Δ BPC + area of Δ APC

`1/2 xx b xx h = 1/2 xx b_1 xx h_1  + 1/2 xx b_2 xx h_2 + 1/2 xx b_3 xx h_3`

`1/2 xx 6 xx 8 = 1/2 xx 8 xx r + 1/2 xx 6 xx r + 1/2 xx 10 xx r`

`24 = 4r + 3r + 5r`

`24 = 12r`

⇒ r = 2

∵ d = 2r

⇒ `d = 2 xx 2`

⇒ d = 4 cm

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
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