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`        Suppose we have given a triangle ∆ABC with O as it's orthocentre and C'as it's circumcentre. Find the distance between them.`
10 months ago

Rohit
15 Points
```							Let O the circumcenter of triangle ABC and G its centroid. Extend OG until a point P such that OG/GP=1/2. We'll prove that P is the orthocenter H.Draw the median AA' where A' is the midpoint of BC. Triangles OGA and PGA are similar, since GP=2GO, AG=2A'G and angle  OGA'=angle PGA. Then angle OA'G =angle PGA and OA' is parallel AP. But OA' is perpendicular perp BC so AP is perpendicular to BC, that is, AP is a height of the triangle.Repeating the same argument for the other medians proves that P lies on the three heights and therefore it must be the orthocenter H.The ratio is \$OG/GH=1/2\$ since we constructed it that way.
```
10 months ago
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### Course Features

• 53 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions