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In this problem, a parallelogram \( ABCD \) is given, and the diagonals intersect at point \( O \). You are tasked with finding the values of \( p \) and \( q \).

### Key Properties:
- In a parallelogram, the diagonals bisect each other. This means that the diagonals are divided into two equal parts by the point of intersection.
- Therefore, \( AO = OC \) and \( BO = OD \).

### Given Information:
- \( AO = 15 \), \( OC = 12 \), \( BO = p + q \), and \( OD = 2p + 9 \).

### From the property of diagonals bisecting each other:
1. \( AO = OC \) implies:
   \[
   15 = 12
   \]
   But this condition appears contradictory, and may indicate either a typo or an intended algebraic relation not yet used.

Can you confirm if any clarification is needed or if the equations should proceed algebraically to reassign any intuitive adjustments?



In fig. ABCD, a parallelogram is given. Find the value of p, q.

Learn how to find the values of p and q in a parallelogram ABCD, where the diagonals bisect each other. This geometry problem involves key concepts such as diagonal bisecting theorem and algebraic relations. Suitable for Grades 8-10.

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