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In a parallelogram ABCD diagonals AC and...

In a parallelogram ABCD diagonals AC and BD intersect at O and AC =12.6 cm and BD = 9.4 cm. Find the measures of OC and OD.

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To solve the problem, we need to find the lengths of OC and OD in the parallelogram ABCD where the diagonals AC and BD intersect at point O. We know that the diagonals of a parallelogram bisect each other. ### Step-by-Step Solution: 1. **Identify the lengths of the diagonals**: - Given: AC = 12.6 cm and BD = 9.4 cm. 2. **Understanding the properties of the diagonals**: - In a parallelogram, the diagonals bisect each other. This means that point O divides each diagonal into two equal parts. - Therefore, OC = OA and OD = OB. 3. **Calculate OC**: - Since AC is bisected at O, we can find OC by taking half of AC. - Formula: OC = 1/2 * AC - Calculation: OC = 1/2 * 12.6 cm = 6.3 cm. 4. **Calculate OD**: - Similarly, since BD is also bisected at O, we can find OD by taking half of BD. - Formula: OD = 1/2 * BD - Calculation: OD = 1/2 * 9.4 cm = 4.7 cm. 5. **Final Results**: - OC = 6.3 cm - OD = 4.7 cm ### Summary: - The lengths of OC and OD are 6.3 cm and 4.7 cm respectively.
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