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Prove that the centre of a circle touchi...

Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines.

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To prove that the center of a circle touching two intersecting lines lies on the angle bisector of the lines, we can follow these steps: ### Step-by-Step Solution 1. **Understand the Setup**: Let the two intersecting lines be denoted as \( RP \) and \( QP \) which intersect at point \( P \). Let \( O \) be the center of the circle that touches both lines \( RP \) and \( QP \) at points \( R \) and \( Q \) respectively. 2. **Identify Tangents**: ...
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