 Hello students, let's work out the following problem. It says in the given figure BD is perpendicular to AC and CE is perpendicular to AB. Prove that triangle AEC is similar to triangle ADB and CA into DB is equal to AB into CE. So let's now move on to the solution. Now in triangles AEC and ADB angle AEC is equal to angle ADB because each is 90 degrees and angle A is equal to angle A because it's a common angle. Therefore by angle angle similarity triangle AEC is similar to triangle ADB. So this proves the first part of the question. Now since triangle EC is similar to triangle ADB the ratio of the corresponding side will be same. Therefore we have AE upon AD is equal to EC upon DB is equal to CA upon BA. Now considering the last two we have EC upon DB is equal to CA upon BA or we can say AB. So from this we have BA into EC is equal to CA into DB. Hence we have proved CA into DB is equal to AB into CE. So this completes the second part also and this question by for now take care have a good day.