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ICSE Class 10 Answered

Find the distance between orthocentre and circumcentre of the triangle with vertices(0,0), (a,0),(0,b).  ans. with steps and diagram
Asked by keshavendu35 | 23 Sep, 2018, 08:05: PM
answered-by-expert Expert Answer
ΔAOB is a right-angled triangle.
 
Hence its Orthocentre will be at Origin(0,0).
 
By using distance formula:
AB (Hypotenuse)= begin mathsize 16px style square root of straight a squared space plus space straight b squared end root end style
Circumcentre of a right angled triangle will be at mid point of hypotenuse.
 
So distance from Circumcentre to Orthocentre will be distance between (0,0) to begin mathsize 16px style open parentheses straight a over 2 comma fraction numerator begin display style straight b end style over denominator begin display style 2 end style end fraction space close parentheses end style.
By using distance formula:


Distance = begin mathsize 16px style square root of straight a squared over 4 plus fraction numerator begin display style straight b squared end style over denominator begin display style 4 end style end fraction end root equals space 1 half square root of straight a squared plus straight b squared end root end style
 
The distance between Orthocentre and Circumcentre of the triangle with vertices(0,0), (a,0),(0,b) is
 Error converting from MathML to accessible text..
Answered by Yasmeen Khan | 25 Sep, 2018, 05:44: PM

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