The length of each side of a square is 3 in. more than the length of each side of a similar square. the sum of the areas of the squares is 425in^2. find the lengths of the sides of the two squares

In the diagram, ab is tangent to c, ab = 4 inches, and ad = 2 inches. find the radius of the circle.

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality

Which of the following are independent events? a) knowing that it is going to rain tomorrow, and bringing an umbrella to schoolb) knowing that you have to get up early tomorrow, and going to bed before 9 p. mc) knowing that it is going to rain tomorrow, and going to bed before 9 p. md) knowing that you have a test in school tomorrow, and studying thw night before