Geo1 - Problems in Geometry(1 1 In a triangle ABC with orthocenter H and circumcircle O prove that < BAH =< OAC 1 2 Let ABC be a triangle with

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Problems in Geometry (1) 1. In a triangle ABC with orthocenter H and circumcircle O prove that < BAH = < OAC . 1 2. Let ABC be a triangle with orthocenter H in which AH, BH, CH meet BC, CA, AB in D, E, F respectively. Prove that HA · HD = HB · HE = HC · HF. 2 3. Let ABC be a triangle with orthocenter H in which AH, BH, CH meet BC, CA, AB in D, E, F respectively. (A ) If ABC is an acute angled triangle, prove that H is the incenter of DEF. 3 (B ) What happens if A is an obtuse angle ? 4. Let ABC be a triangle with incenter I and excenters I a , I b , I c . (A) Prove that I is the orthocenter of the triangle I a I b I c . (B) Prove that the circumcircle of a triangle passes through the midpoint of a line segment joining any two of the excenters. (C) Prove that the circumcircle of a triangle passes through the midpoint of a line segment joining the incenter with any one of the excenters. 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/14/2011 for the course MATH 373 taught by Professor Cemtezer during the Spring '11 term at Middle East Technical University.

Page1 / 2

Geo1 - Problems in Geometry(1 1 In a triangle ABC with orthocenter H and circumcircle O prove that < BAH =< OAC 1 2 Let ABC be a triangle with

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online