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.
