2021 · Q84
Consider the following for the next two (02) items that follow : ABC is triangle in which AB = AC and D is any point on BC. Which one of the following is correct ?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AAB² − AD² = AD × BD
- BAC² − AD² = BD × CD
- CAB² − AD² = 2AD × BD
- DAC² − AD² = 2BD × CD
Explanation
By Stewart's theorem on cevian AD with AB = AC = a: a²·CD + a²·BD = BC·(AD² + BD·CD). Since BD + CD = BC, a² = AD² + BD·CD, i.e. AC² − AD² = BD × CD. This is option (b).