Question

in triangle △ABC , point D is between points A and B, and point E is between points B and C. Point Y is the incenter of the triangle, YD¯¯¯¯¯⊥AB¯¯¯¯¯ , and YE¯¯¯¯¯⊥BC¯¯¯¯¯ . DB=45 and YB=51 . What is YE ? Could you show me how to solve it also??

Answer 1

To find YE, we can use the fact that triangle △AYB is an equilateral triangle. Therefore, YE = YB = 51.

Step-by-step explanation:

To find YE, first let's look at triangle △ABY. Since YD¯¯¯¯¯⊥AB¯¯¯¯¯ and YE¯¯¯¯¯⊥BC¯¯¯¯¯, angle YDB = 90° and angle YEB = 90°. This means that angles YBA and YAC are equal, as they are corresponding angles. Since triangle △ABY is isosceles, YB is also equal to YA.

Therefore, we have a triangle where two sides are equal. This means that the angles opposite those sides are also equal. So angle YAB is equal to angle YBA. Using this information, we can conclude that triangle △AYB is an equilateral triangle.

In an equilateral triangle, all sides are equal. Therefore, YE = YB = 51.