Q002 Ex-central triangle
Outlines
-
Q01 |
What is ex-central triangle ?
- Q02 | Properties of ex-central triangle
- Q03 | Pedal triangle
- Q04 | Diagram : Ex-central triangle
- Q05 | Diagram : Pedal triangle
- Q06 | Five centers of triangle ANC
- Q07 | Reference
- Q02 | Properties of ex-central triangle
1. What is Ex-central triangle
Construction
- 1. Draw a triangle ABC ?
- 2. Draw three es-centers J, K, L of triangle ABC
- 3. Join the centers J, K, L as vertices of the triangle JKL
- 4. Triangle JKL is called ex-central triangle
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2. Properties of ex-central triangle
Properties
- 1. Prove that J, C, K are colinear
- 2. Prove that I is the in-center of triangle ABC
- 3. Prove that I is also the orthocenter of triangle JKL
- 4. Prove that ABC is pedal triangle of triangle JKL
- 5. Prove that the tangent length is s from A to ex-circle
- The proof can be found in reference
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3. Pedal triangle
- Prove that ABC is pedal triangle of triangle JKL
- The proof can be found in the reference
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4. Diagram : Ex-central triangle
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5. Diagram : Pedal triangle
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6. Five centers of triangle ABC
- Centroid
- Circum-center
- Ex-center
- In-center
- Ortho-center
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7. Reference
- Prove that J, C, K are colinear.
- Prove that I is the in-center of triangle ABC.
- Prove that I is also the orthocenter of triangle JKL.
- Prove that ABC is pedal triangle of triangle JKL.
- GE 18 03 | - Ex-center : Concurrent of bisectors of triangle
- GE 18 04 | - In-center of triangle ABC is ortho-center of triangle JKL
- GE 18 05 | - The tangent from A to ex-circle is s
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