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In figure, DE || AB and BD || BEF. Prove...

In figure, `DE || AB and BD || BEF.` Prove that `DC^2=CF xx AC`

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To prove that \( DC^2 = CF \times AC \), we will use the properties of similar triangles and the Basic Proportionality Theorem (also known as Thales' theorem). ### Step-by-Step Solution: 1. **Identify the triangles**: We have triangle \( ABC \) with line \( DE \) parallel to \( AB \) and line \( BD \) parallel to \( BEF \). 2. **Apply the Basic Proportionality Theorem in Triangle \( ABC \)**: Since \( DE \parallel AB \), by the Basic Proportionality Theorem, we have: ...
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