Sir, I think there is a small mistake in the article, you proved the triangles PQA & PQB are congruent using the SAS congruency test but stated it as hypotenuse-side congruency, the rest of the article is fine.

Late to the party, but Sir, Is the point which is equidistant from all three sides both the incentre and circumcentre. I knew incentre( point lying on angle bisectors is equidistant from all 3 sides), but does this holds true for Circumcentre as well?

thanks

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Sir, I think there is a small mistake in the article, you proved the triangles PQA & PQB are congruent using the SAS congruency test but stated it as hypotenuse-side congruency, the rest of the article is fine.

Right you are! Thanks.

regards

J

Late to the party, but Sir, Is the point which is equidistant from all three sides both the incentre and circumcentre. I knew incentre( point lying on angle bisectors is equidistant from all 3 sides), but does this holds true for Circumcentre as well?

No, the circumcentre is equidistant from all three *vertices* as mentioned above, while the incentre is equidistant from all three *sides*.

regards

J

Thank you for whatever you have done for us till now! Your posts and insights on PG and off here are GOLDD! Indebted.