2. Rectangle ABCD has vertices at A(0, 0), B(0, 1), C(4, 1), and D(4, 0). The points E and F are on the x-axis so that AEAB is similar to ACDF (that is, ZEAB = ZCDF, ZEBA = ZCFD, and ZBEA = LFCD). Let P be the point of intersection of the lines extending EB and FC. Show that P lies on the circle of radius 2 centred at (2, 1). B C EA D4. Find all right-angled triangles whose side lengths form an arithmetic sequence. Because of triangle similarity, there are infinitely many such triangles. For example, if a triangle with side lengths a, b, and c satisfies the given conditions, then the triangle with side lengths 2a, 26, and 2c also satisfies the conditions. You only need to give one triangle for each similarity "type". ]5. In AABC, we label AB = c, BC = a, and CA = b. Show that the area of AABC is equal to 02 sin A sin B 2 sin(A + B) This result says that we can determine the area of a triangle using a known side length and the measures of the two angles to which it is incident. You might like to think about the signicance of this as it relates to angle-side-angle congruence, as well as other area formulas and other congruence conditions