Problem
GEO-B1-M08-P006 Altitudes and a Circle
#6
★★★☆☆ Level 3 of 5
In triangle \(ABC\), points \(D\) and \(E\) are the feet of the altitudes from \(B\) and \(C\). Prove that points \(B,C,D,E\) lie on one circle.
Find two right angles standing on \(BC\).
Since \(BD\perp AC\), we have \(\angle BDC=90^\circ\). Since \(CE\perp AB\), we have \(\angle BEC=90^\circ\). Hence points \(D\) and \(E\) lie on the circle with diameter \(BC\). Therefore \(B,C,D,E\) are cyclic.
Mixes altitudes with a circle with a diameter.