Answer :

Here, Clearly I and III are correct.

Let us check for II statement

**Construction:** Let B and C be the centers of two circles having radii 10cm and 17 cm respectively and let AD be the common chord cutting BC at E.

Here,

AE = ED = 8cm

Now, in ΔABE

BE^{2} = AB^{2} – AE^{2}

BE^{2} = (10)^{2} – (8)^{2}

BE^{2} = 100– 64 = 36

BE = 6cm

Now, in ΔAEC

EC^{2} = AC^{2} – AE^{2}

EC^{2} = (17)^{2} – (8)^{2}

EC^{2} = 289– 64 = 225

EC = 25cm

Here,

BC = BE + EC = 6 + 15 = 21cm

But, it is given BC = 23cm

∴ Statement II is false

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