2017 · Q67
If PL, QM and RN are the altitudes of triangle PQR whose orthocentre is 0, then Q is the orthocentre of the triangle
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AOPQ
- BOQR
- CPLR
- DOPR
Explanation
O is the orthocenter of △PQR, so PL ⊥ QR, QM ⊥ PR, RN ⊥ PQ. In △OPR: OQ ⊥ PR (Q lies on QM) is the altitude from O, and RQ ⊥ OP (R lies on RN, O lies on PL) is the altitude from R. Their intersection Q is the orthocenter of △OPR. Hence option (D) OPR.