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Fill in the blanks in the following so that each of the following statements is true.
If altitudes CE and BE of a triangle ABC are equal,then AB = .......

A
AC
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Solution
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Correct option is A. AC

In $$\triangle ABC,$$
$$BF\perp AC$$ and $$CE\perp AB$$ [ Given ]
$$BF=CE$$ [ Given ]
Area of $$\triangle ABC=\dfrac{1}{2}\times AB\times CE$$ ---- ( 1 )

Area of $$\triangle ABC=\dfrac{1}{2}\times BF\times AC$$ ---- ( 2 )

Comparing ( 1 ) and ( 2 ),
$$\Rightarrow$$ $$\dfrac{1}{2}\times AB\times CE=\dfrac{1}{2} BF\times AC$$

$$\Rightarrow$$ $$AB\times CE= CE\times AC$$ [ Since, $$BF=CE$$ ]

$$\therefore$$ $$AB=AC$$

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