A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see given figure). Find the sides AB and AC. explain this some in a little easy maNNER.PLS EXPERTSS
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in this case I WL use the concept of tangent of a circle.so let the unknown side be x+8 and x+6cm respectively. so by the Heron's formula, 2s=2x+28cm.
or,s=x+14cm. then area of the triangle=√s(s-a)(s-b)(s-c).or,area =√x+14(48x).…..............(1)
and total area of the triangle=1/2×4(14+x+8+x+6)or,56+4xcm²...................(2)
comparing both the sides,
(x+14)(48x)=(56+4x)².
or, 32x²+224x-3136=0
or,x²+7x-98=0
or,solving the quadratic equation we get,x=7cm.thus the sides are 15and 13cm.
or,s=x+14cm. then area of the triangle=√s(s-a)(s-b)(s-c).or,area =√x+14(48x).…..............(1)
and total area of the triangle=1/2×4(14+x+8+x+6)or,56+4xcm²...................(2)
comparing both the sides,
(x+14)(48x)=(56+4x)².
or, 32x²+224x-3136=0
or,x²+7x-98=0
or,solving the quadratic equation we get,x=7cm.thus the sides are 15and 13cm.
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