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A triangle ABC is drawn to circumscribe ...

A triangle `ABC` is drawn to circumscribe a circle of radius `4cm` such that the segments `BD` and `DC` into which `BC` is divided by the point of contact `D` are of lengths `6cm` and `8cm` respectively. Find the lengths of the sides `AB` and `AC`.

Text Solution

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Length of two tangents drawn from the same point to the circle are equal.
`CF = CD = 6 cm`
` BE = BD = 8 cm`
` AE = AF = x`
We observed that,
`AB = AE + EB = x + 8`
`BC = BD + DC = 8 + 6 = 14`
`CA = CF + FA = 6 + x`
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