1. Using the Pythagorean theorem, we can calculate DC. BC^2 = BD^2 + DC^2 We don't know the lenght of BD. On the picture, there are 3 right triangles. Using the theorem on 2 other triangles, we get: (1)AC^2 = BA^2 + BC^2 (2)BA^2 = BD^2 + AD^2 Replace the BA^2 in formula (1) with its addends. AC^2 = BD^2 + AD^2 + BC^2 AC = AD + DC (AD + DC)^2 = BD^2 + AD^2 + BC^2 BD^2 = (AD + DC)^2 - AD^2 - BC^2 BD^2 = BD^2 (AD + DC)^2 - AD^2 - BC^2 = BC^2 - DC^2 AD^2+2AD×DC+DC^2-AD^2-BC^2=BC^2-DC^2 2AD×DC + 2DC^2 = 2BC^2 10DC + 2DC^2 = 2×36 2DC^2 + 10DC - 72 = 0 According to quadratic formula: DC = 4 ; DC = -9 Length can't be negative: DC = 4.
2. Segment that's the projection of QT on RT is ST.
3. . Segment that's the projection of ST on QT is UT.
