In the plane rectangular coordinate system, points a and B are two moving points on the positive half axis of X axis and Y axis respectively The bisectors of ∠ YAB and ∠ Xba intersect at point P. when AB moves, does the size of ∠ P change? Please explain the reason

In the plane rectangular coordinate system, points a and B are two moving points on the positive half axis of X axis and Y axis respectively The bisectors of ∠ YAB and ∠ Xba intersect at point P. when AB moves, does the size of ∠ P change? Please explain the reason

No matter how AB moves, the size of angle P is always 180-45 = 135

The plane rectangular coordinate system B is a point on the positive half axis of X, the point a is in a quadrant, D is the midpoint of AB, the ordinate of point a is 4, and the function formula of OD is y = 1 / 2x, so the coordinate of point D can be obtained

Draw a right triangle auxiliary analysis, you can get D point ordinate is a point ordinate general, that is, 2, so as to get x = 1 / 4

As shown in the figure, in the plane rectangular coordinate system, the straight line AB passes through the first, second and third quadrants and intersects the x-axis and y-axis at two points a and B respectively
It is known that ab = AC = 10, s △ ACD = 24, and B (0,6),
(1) Verification: △ AOB ≌ △ ADC; find the coordinates of point a
(2) Connect OD, AE, verify: OD ⊥ AE
(3) Point m is the moving point on line OA, make ∠ NME = ∠ ome, and Mn intersects ad at point n. when point m moves, find the value of Mn divided by Mo + nd

If "the line CD ⊥ AB is at D, intersecting x-axis and y-axis at O and e respectively" is changed to "the line CD ⊥ AB is at D, intersecting x-axis and y-axis at C and e respectively", then:
(1) In △ AOB and △ ADC, ∠ AOB = ∠ ADC, ∠ Bao = ∠ CAD, ab = AC, so △ AOB ≌ △ ADC
So: s △ AOB = s △ ACD = 24 = | Xa | * Yb / 2 = - 3xa