A circle through two perpendicular feet

A circle through two perpendicular feet

Secondary 4
5 marks
TGM Original Questions

In acute triangle \(ABC\), \(D\) lies on \(AC\) with \(BD\perp AC\), and \(E\) lies on \(AB\) with \(CE\perp AB\).

  1. Prove that \(B,C,D,E\) lie on one circle.[3]
  2. State the centre and diameter of this circle, giving a reason.[2]

Solution:

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Answer:(a) Both right angles stand on diameter \(BC\). (b) Diameter \(BC\); centre its midpoint.

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