A circle is inscribed in a triangle ABC touching the side AB at D such that AD =5, BD=3 - Maths - Solution of Triangles

Question

A circle is inscribed in a triangle ABC touching the side AB at D
such that AD =5, BD=3 If angle A is 60o then find length
BC

Ghanshyam Dhakar · Accepted Answer

Dear
student,
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Tangents drawn from external point to a circle are equal in lengthBD = BF=3CF =CEAD=5=AEusing cos A = b2+c2-a22bccos 60° = AE+CE2+AD+BD2-BF+CF22AE+CEAD+BD⇒12= 5+CE2+5+32-3+CE225+CE8⇒12= 25+CE2+10CE+64-9-CE2-6CE25+CE8⇒12= 4CE+80165+CE⇒165+CE=8CE+160⇒25+CE=CE+20⇒CE = 10=CFthen, BC = CF+BF=10+3=13 units

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A circle is inscribed in a triangle ABC touching the side AB at D such that AD =5, BD=3. If angle A is 60o then find length BC.

A circle is inscribed in a triangle ABC touching the side AB at D such that AD =5, BD=3. If angle A is 60^o then find length BC.