Draw a square of 4 cm. Constuct angle bisectors of 4 angles.Let all meet at O. measure AO and OC . Then $A O^{2} + O C^{2}$ =

8

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4

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16

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32

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Solution

The correct option is A $16$
Since side of square is 4 cm i.e. AB = BC = CD = AD = 4 cm
By applying pythagoras theorem in triangle ABC, we get
${A C}^{2} = {A B}^{2} + {B C}^{2} {A C}^{2} = 4^{2} + 4^{2} A C = 4 \sqrt{2} N o w, A O = C O = \frac{4 \sqrt{2}}{2} A O = C O = 2 \sqrt{2} {A O}^{2} = {C O}^{2} = 8 {A O}^{2} + {C O}^{2} = 16$
So, option C is correct.

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Draw a square of 4 cm. Constuct angle bisectors of 4 angles.Let all meet at O. measure AO and OC . Then AO2+OC2=

The correct option is A 16Since side of square is 4 cm i.e. AB = BC = CD = AD = 4 cmBy applying pythagoras theorem in triangle ABC, we get AC2=AB2+BC2AC2=42+42AC=4√2Now,AO=CO=4√22AO=CO=2√2AO2=CO2=8AO2+CO2=16So, option C is correct.

Draw a square of 4 cm. Constuct angle bisectors of 4 angles.Let all meet at O. measure AO and OC . Then $A O^{2} + O C^{2}$ =