2026 · Q89
For the next two (02) items that follow : PQR is a triangle such that QP = QR = 15 cm and PR = 18 cm. PN, QM and RT are the altitudes of the triangle which intersect at O. What is QT : QO equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A3 : 4
- B4 : 5
- C3 : 5
- D1 : 2
Explanation
Set M = (0, 0) (midpoint of PR), P = (−9, 0), R = (9, 0), Q = (0, 12) since QM = √(15² − 9²) = 12. The altitude from R to PQ meets PQ at T = (−63/25, 648/75), giving QT = √[(63/25)² + (84/25)²] = 105/25 = 4.2. The orthocenter O lies on x = 0 at the intersection with the altitude from P, y = 27/4, so QO = 12 − 27/4 = 21/4 = 5.25. Thus QT : QO = 4.2 : 5.25 = 4 : 5, option B.