Question

Let ABCD be a square and let AC = BD = 10 cm. Let AC and BD intersect in O. Find OC and OD.

Answer 1

Since ABCD is a square

Therefore all its sides are equal

Therefore AC^2=AB^2+BC^2(using pythagoras theorem)

AC= underroot of 10^2+10^2

AC=10underroot 2

OC=AC/2

And OC=OD(since diagonals of square perpendicularly bisect each other)

Therefore OC=OD=5 underroot2

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Answer 2

Answer:

OC = 5 cm, OD = 5 cm

Step-by-step explanation:

Given, ABCD is a square.

Then, AB = BC = CD = DA

Now,

AC = BD = 10 cm

Given, AC and BD intersect at O.

Therefore, OA = OB = OC = OD = 10/2 cm (since AC and BD are equal and the diagonals of square perpendicularly bisect each other)

Therefore, OC and OD = 5 cm.

Hope it helps!