Competition problem — Geometry — Maths Olympiad Prep

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Geometry Difficulty 5.7 AIME, harder Prove it

A line intersects the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=\alpha$ at $A_{1} 、 B_{1}$ , and intersects the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=\beta$ at $A_{2} 、 B_{2}$ . Prove: $\left|A_{1} A_{2}\right|=\left|B_{1} B_{2}\right|$ .

Solution

None

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