Algorithm 22.A: Similar triangles

Given the lengths of one triangle, $s_1$, $s_2$ and $s_3$ and three lengths of another triangle, $t_1$, $t_2$ and $t_3$, describe an algorithm that determines if the two triangles are similar.

Algorithm 22.B: Co-linear test

Input: three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$.
Output: 'yes' or 'no'.

Given points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$, describe an algorithm that determines if the three points are co-linear, meaning, they all fall on the same line in a plane.

Algorithm 22.C: Right-angled triangle test

Input: three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$.
Output: 'yes' or 'no'.

Given points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$, describe an algorithm that determines if the three points define a right-angled triangle.

Algorithm 22.D Find the circle passing through three points

Input: three points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$.
Output: either 'yes' or 'no', and if 'yes', the center $(x, y)$ and the radius $r$.

Given points $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$, describe an algorithm that determines if these three points falls on a circle, and if they do, find the center $(x, y)$ and the radius $r$ of that unique circle that passes through all three points.