Problem
GEO-B2-M10-P002 Two Altitudes
#2
★★☆☆☆ Level 2 of 5
In triangle \(ABC\), points \(D\) and \(E\) are the feet of the altitudes from \(B\) and \(C\). Prove that \(B,C,D,E\) lie on one circle.
Find two right angles subtending the same segment.
Since \(BD\perp CD\), \(\angle BDC=90^\circ\). Since \(BE\perp CE\), \(\angle BEC=90^\circ\). Thus \(D\) and \(E\) lie on the circle with diameter \(BC\), so \(B,C,D,E\) are concyclic.
The key is to see the circle with diameter \(BC\).