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In the adjoining figure, BX and CY are ...

In the adjoining figure, BX and CY are the bisectors of `angle ABC and angle ACB` respectively. If `AB=AC` and BY=4 cm, then find the lengths of AX.

Text Solution

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In `Delta ABC, AB=AC, :. angleABC= angle ACB`
`or, (1)/(2) angle ABC=(1)/(2)angle ACB`
`or, angle ABX= angle BCY [ :. BY and CY` are the bisectors of `angle ABC and angle ACB` respectively.]
`:.` by the converse theorem of theorem 35, are AC= arc Bu =4 cm [ `:.` BY 4 cm (given)]
Hence the lengths of AX = 4 cm.
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