Height and median of equilateral triangle
Q01. Diagram
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Q02. Pedal triangle of equilateral triangle
Construction
- Draw an equilateral triangle
- Draw three heights AD, BE, CF
- Then AD, BE, CF are also the medians
Proof
- Right angle ACF and angle ACF = 30 degrees
- Hence AF = AC/2
- Hence AF = BF
- Hence CF is also median
- 1. AD, BE, CF are also angle bisectors
- 2. AD, BE, CF are also side bisectors
- 3. Centroid, orth-center, in-center and circum-center at same point O
- 4. Triangle DEF is pedal triangle
- 5. Four centers of pedal triangle DEF are at same point O
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Q03. Questions
Questions
- 1. What is pedal triangle ?
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