Figure 115 : Otho-center, centroid and circum-center
Q01. Diagram
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Q02. Otho-center, centroid and circum-center are colinear
Construction
- Draw Ortho-center O
- Draw centoid G
- Draw circum-center V
Proof
- Join O,G,V
- Let M be mid-point of GO and N be mid-point of CG
- Hence MN = CO/2 and MN parallel to CO
- Also VF = CO/2 (GE 16 06)
- Angle MCN = angle GFV
- Hence triangle MGN and GVF are congruent (SAS)
- AGF is stri=aight line and angle FGV = angle MGN
- Hence O,G, V are colinear
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Q03. Questions
Questions
- 1. What is circum-center ?
- 2. What is centroid ?
- 3. What is orthocenter ?
- 4. Verify by construction to show O, G, V are colinear
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