Li Bowers
02/27/2023 · High School
[12] ABC is an inscribed triangle in a circle where \( A C \gtrdot A B, D \in \overrightarrow{B C} \), where \( \triangle \mathrm{D} \wedge \mathrm{B} \). Draw \( \overrightarrow{A N} \) a tangent to the circle at \( \triangle \) and cuts \( \overrightarrow{C B} \) at \( N \) Prove that: \( \mathrm{BN}: \mathrm{DC}=(\mathrm{AN})^{2}:(\mathrm{CA})^{2} \)
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To prove \( \mathrm{BN} : \mathrm{DC} = (AN)^2 : (CA)^2 \), use the Power of a Point theorem and properties of similar triangles. The final ratio is derived from the relationship between \( AN \), \( NB \), and \( DC \).
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