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If P divides OA internally in the ratio ?\index{1}:?\index{2} and Q divides OA  extrnally in the  ratio ?\index{1}:?\index{2} , them prove that OA is the harmonic mean   of OP and OQ.

If P divides OA internally in the ratio ?\index{1}:?\index{2} and Q divides OA  extrnally in the  ratio ?\index{1}:?\index{2} , them prove that OA is the harmonic mean   of OP and OQ.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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  If P divides OA internally in the ratio ?\index{1}:?\index{2} and Q divides OA
 extrnally in the  ratio ?\index{1}:?\index{2} , them prove that OA is the harmonic mean 
 of OP and OQ.
and If the circumcenter of an acute-angled triangle lies at the origin and 
the centroid is the middle point of the line joining the points (a\power{2}+1,a\power{2}+1)
 and (2a, -2a), then find the orthocenter.

If P divides OA internally in the ratio λ₁ : λ2 and Q divides OA extrnally in the ratio λ₁ : λ2, them prove that OA is the harmonic mean of OP and OQ. and If the circumcenter of an acute - angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a² + 1, a² + 1) and (2a, −2a), then find the orthocenter.
Transcribed Image Text:If P divides OA internally in the ratio λ₁ : λ2 and Q divides OA extrnally in the ratio λ₁ : λ2, them prove that OA is the harmonic mean of OP and OQ. and If the circumcenter of an acute - angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a² + 1, a² + 1) and (2a, −2a), then find the orthocenter.
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