2021 · Q87
Consider the following for the next three (03) items that follow : ABC is a triangle with AB = 1.6 cm, BC = 6.3 cm and CA = 6.5 cm. Let P and Q be the mid-points of AB and BC respectively. What is AQ² + CP² equal to ?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AAC²
- B1.2AC²
- C1.25AC²
- D1.5AC²
Explanation
By Apollonius on median AQ: AB² + AC² = 2AQ² + BC²/2 gives 2.56 + 42.25 = 2AQ² + 19.845, so AQ² = 12.4825. Similarly for median CP: CA² + CB² = 2CP² + AB²/2 gives CP² = 40.33. Their sum is 52.8125 = 1.25 × 42.25 = 1.25AC². This is option (c).