Figure 129 : Ex-center
Q01. Diagram
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Q02. Ex-center
Construction
- Draw a triangle ABC
- Draw bisector of angle A
- Draw bisector of external angle B
- Draw bisector of external angle C
- Draw height CF to AB
- Bisectors are concurrent and meet at E which is the ex-center
- Let EP perpendicular to AB
- Let EQ perpendicular to AC
- Let ER perpendicular to BC
- Since AE is angle bisector, hence EP = EQ
- Since BE is angle bisector, hence EP = ER
- Since ER = EQ, Hence CE is also angle bisector
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Q3. Tangent length from A to ex-circle
Tangent length from A to ex-circle is s
- Let EP perpendicular to AB
- Let EQ perpendicular to AC
- Then AP = AQ
- AP = AB + BP and AQ = AC + CQ
- AP + AQ = AB + BP + AC + CQ
- Since BC = CQ + BP
- Hence 2*AP = AB + BC + CA = 2*s
- Hence AP = s
- r1 = s*tan(A/2)
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Q04. Reference
- Program 04 08
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Program 03 02
- See keyword : Ex-center
- See keyword : ex-central triangle
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Q05. Questions
- What is ex-circle ?
- What is ex-central triangle ?
- Describe the properties of ex-central triangle
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