Pls prove it:the reflection of orthocentre of tria

Question

Pls prove it:the reflection of orthocentre oftriangle in any one side of the triangle lies on the circumcircle of the triangle

Vikas TU · Accepted Answer

Dear Student,Though it is hard to prove without diagram:-H' = refection of H using line ABD is the second end of CD.ang CBD = 90 (as an inscribed angle subtended by a diameter),=>BD perpendicular to BC. AH is an altitude in ABC, is perpendicular to BCso AH parallel to BD.BH is an altitude while ang CAD = 90. Therefore AD parallel to BH.ADBH is a parallelogram. AB and DH intersect at common midpoint so midpoint Mc of AB lies on DHand HMc = McD.C' be the foot of the altitude CH HC' = C'H'.In triangle DHH' C'Mc is parallel to DH': C'Mc parallel toDH'. And, since ang BC'C = 90, so too ang DH'H = 90. ang DH'C =90 and subtended by CD.so,H' lies on the circumcircle. [proved]Cheers!!Regards,Vikas (B. Tech. 4th yearThapar University)

Analytical Geometry> Pls prove it:the reflection of orthocentr...

Pls prove it:the reflection of orthocentre oftriangle in any one side of the triangle lies on the circumcircle of the triangle

sahil suman , 7 Years ago

Vikas TU

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Analytical Geometry> Pls prove it:the reflection of orthocentr...

Pls prove it:the reflection of orthocentre oftriangle in any one side of the triangle lies on the circumcircle of the triangle

sahil suman , 7 Years ago

Vikas TU

Provide a better Answer & Earn Cool Goodies

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