The lengths of the tangents drawn from the vertices A , B , C to the incircle of △ A BC are 5, 3, 2 respectively. If the lengths of the parts of tangents with in the triangle which are drawn parallel

Question

The lengths of the tangents drawn from the vertices A , B , C to the incircle of △ A BC are 5, 3, 2 respectively. If the lengths of the parts of tangents with in the triangle which are drawn parallel to the sides BC , CA , AB of the triangle to the incircle be α , β , γ respectively, then [ α + β + γ ] where ( [ □ ] is G.I.F. is)

TestHub · Accepted Answer

​ r = ( S − a ) tan 2 A ​ S − a r ​ = A P r ​ ⇒ S − a = 5 , S − b = 3 , S − c = 2 ⇒ S = 10 ⇒ a = 5 , b = 7 , c = 8 a x ​ + b y ​ + c z ​ = 1 ⇒ 5 α ​ + 7 β ​ + 8 γ ​ = 1 α = S tan 2 A ​ r a ​ , β = S tan 2 B ​ r b ​ , γ = S tan 2 C ​ rc ​ α = S ( S − a ) a ​ , β = S ( S − b ) b ​ , γ = S ( S − c ) c ​ α = 10 5 × 5 ​ , β = 10 3 × 7 ​ , γ = 10 2 × 8 ​ α + β + γ = 10 25 + 21 + 16 ​ = 10 62 ​ ⇒ [ α + β + γ ] = 6 ​

Mathematics - Properties of Triangle Question with Solution | TestHub

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JEE Advanced 2028 (Class 11)