In square $□ A B C D$ , join $A C$ . Let $O$ be midpoint of $A C$ and $A O ⊥ B D$ .
Which one of following is true?

A O

passes through

D

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A O

cuts

C D

between

C, D

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A O

cuts

B C

in point other than

B, C

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A O

passes through

C

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Solution

The correct option is D $A O$ passes through $C$ .
According to property of square, diagonals bisect each other at right angle.
Since, AO is perpendicular to BD and O is midpoint of AC. So, AO must pass through point C.
Hence, Option D is correct.

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Which of the following statement is correct?

BO and CO are respectively the bisectors of angle B and C of ∆ABC. AO produced meets BC at P. Show that AO/BP = AO/OP , AC/CP = AO/OP ,

AB/AC = BP/PC , AP is the bisector of angle BAC.

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Q. In a parallelogram ABCD, diagonals AC and BD intersect at O. Which of the following is equal to AO?

BO and CO are respectively the bisectors of $∠ B$ and $∠ C$ of $Δ A B C$ . AO produced meets BC at P.

Show that [4 MARKS]

(i) $\frac{A B}{B P} = \frac{A O}{O P}$

(ii) $\frac{A C}{C P} = \frac{A O}{O P}$

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(iv) $A P$ is the bisector of $∠ B A C$ .

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In square □ABCD, join AC. Let O be midpoint of AC and AO⊥BD.Which one of following is true?

The correct option is D AO passes through C.According to property of square, diagonals bisect each other at right angle.Since, AO is perpendicular to BD and O is midpoint of AC. So, AO must pass through point C.Hence, Option D is correct.

In square $□ A B C D$ , join $A C$ . Let $O$ be midpoint of $A C$ and $A O ⊥ B D$ .
Which one of following is true?

The correct option is D $A O$ passes through $C$ .
According to property of square, diagonals bisect each other at right angle.
Since, AO is perpendicular to BD and O is midpoint of AC. So, AO must pass through point C.
Hence, Option D is correct.