Krishna
0

Step 1: Note down the given points and observe the diagram


Step 2: Calculate the lengths of the triangle by using the distance formula


d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2\ }\ -\ y_1\right)^2}\


EXAMPLE: Given points (2, 1)(10, 7)

r\ =\ \sqrt{\left(10\ -\ 2\right)^2\ +\ \left(7-1\right)^2}

r=\sqrt{64+36}


r =\sqrt{100}


Step 3: Verify is it a right angle triangle or not.

          NOTE: All triangles In a semi circle are right angle triangles.  


Step 4: Apply the Pythagorean theorem to calculate the unknown values

              NOTE:  (PR)^2 = (PQ)^2 + (QR)^2


EXAMPLE: (PR)^2 = (a + 3)^2 + (4 - 2)^2 = a^2 + 6a + 9 + 4 = a^2 + 6a + 13 

                  (PQ)^2=(9+3)^2+(10-2)^2=144+64=208

                   (QR)^2 = (a - 9)^2 + (4 -10)^2 = a^2 - 18a + 81 + 36 = a^2 - 18a + 117 


                    (PR)^2 = (PQ)^2 + (QR)^2

                  a^2+6a+13=208+a^2-18a+117

                      24a = 312 

                        a = 13