Prove that every circle passing through a fixed point and having its centre on a fixed straight line must pass through another fixed point
Please help me understand the question and provide me with a geometric proof
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2Well, draw a picture. Can you work out where the other fixed point must be? – lulu Apr 01 '19 at 12:29
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On the symmetrical opposite to the fixed point – Rishabh Shetty Apr 01 '19 at 12:32
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2Sure. The reflection. Once you have identified that point, it should be easy to prove the claim. – lulu Apr 01 '19 at 14:29
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Any hint please – Rishabh Shetty Apr 01 '19 at 14:58
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If $P$ is the point, $\overline P$ the reflection, let $X$ be the point on the line connecting $P,\overline P$ and let $Q$ be a random point on the fixed line. Then show that the two triangles $\Delta PXQ$, $\Delta \overline PXQ$ are congruent, – lulu Apr 01 '19 at 15:11
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Can you please provide a figure as I can't understand the triangles you are talking about – Rishabh Shetty Apr 01 '19 at 15:19
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1Please make an effort. – lulu Apr 01 '19 at 15:20
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To be clear: $X$ is the point of intersection between the given fixed line and the line connecting $P,\overline P$. It it the midpoint of the segment $P\overline P$. The rest you should be able to do on your own. – lulu Apr 01 '19 at 15:22
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Ok thanks for your help – Rishabh Shetty Apr 01 '19 at 15:28