As shown in the figure, it is known that point O is a point on the hypotenuse of RT △ ABC, with point o as the center and OA length as the radius, the center O and BC are tangent to point E As shown in the figure, we know that the point O is a point on the hypotenuse AC of ABC of RT triangle. With the point o as the center and the OA length as the radius, the center O and BC are tangent to point E and intersect with AC at point D, connecting AE. (1) proof: AE bisection angle CAC (2) explore the quantitative relationship between angle 1 and angle C in the figure Just ask the second question, the first question I know

2 ∠ 1 + ∠ C = 90 °, Tanc = root 3 / 3 ∵ ∠ EOC is the outer angle of △ AOE, ∵ 1 + ∠ AEO = ∠ EOC, ∵ 1 = ∠ AEO, ∵ OEC = 90 ° and ∵ 2 ∠ 1 + ∠ C = 90 ° when AE = CE, ∵ 1 = ∠ C, ∵ 2 ∠ 1 + ∠ C = 90 °
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RELATED INFORMATIONS

1. As shown in the figure, in the known RT △ ABC, the ⊙ o cross bevel BC with ab as the diameter is at point D, and E is the midpoint of AC. connect ed and extend the extension line of intersection AB at point F. (1) prove that De is the tangent of ⊙ o; (2) if ⊙ f = 30 ° AB = 4, find the length of DF and ef
2. Given that the circle C and the y-axis intersect at two points m (0. - 2), and the center of the circle C is on the straight line 2x-y-6 = 0, the equation of circle C is obtained
3. It is known that the circle C passes through two points a (3.2) and B (1.6), and the center of the circle is on the straight line y = 2x (1): find the equation of circle C（ It is known that the circle C passes through two points a (3.2) and B (1.6), and the center of the circle is on the straight line y = 2x (1): find the equation of the circle C (2): if the straight line L passes through P (1.3) and is tangent to the circle C, find the equation of the straight line L
4. If the center of circle C on the straight line 2x-y-7 = 0 intersects with y axis at two points a (0, - 4), B (0, - 2), then the equation of circle C is?
5. The equation of the circle whose center is on the line 2x + y = 0 and tangent to the point (2, - 1) with the line x + Y-1 = 0 is______ ．
6. The circle C with the center of the circle on the straight line 2x-y-7 = 0 intersects at two points a (0-4) B (0-2) on the Y axis to find the equation of circle C,
7. It is known that ⊙ C passes through points a (2,4) and B (3,5), and the center of circle C is on the line 2x-y-2 = 0. (1) find the equation of ⊙ C; (2) if the line y = KX + 3 and ⊙ C always have a common point, find the value range of real number K
8. It is known that the center of circle C is on the straight line y = 2x + 6 and passes through points a (0. - 1), B (- 2,3). Find the vertical bisector of line a and B
9. If the image of the first-order function y = KX + B and the image of the function y = 1 / 2 x + 1 are symmetric about the Y axis, then the expression of the first-order function is?
10. If the image of the first-order function y = KX + B (K ≠ 0) and the function y = 12x + 1 is symmetric about the x-axis and the intersection point is on the x-axis, then the expression of the function is as follows:___ ．
11. As shown in the figure, in RT △ AOB, ∠ B = 40 °, take OA as radius, O as center, make ⊙ o, intersect AB at point C, intersect ob at point D. calculate the degree of CD
12. As shown in the figure, in RT △ AOB, the circle AB with radius OA intersects at point C. If Ao = 5, OB = 12, the length of BC is obtained
13. In the R T triangle AOB, ∠ o = 90 degrees, OA = 6, OB = 8, take o as the center of the circle, OA as the radius, make the circle AB to C, and find the length of BC?
14. As shown in the figure, in RT △ AOB, the circle AB with radius OA intersects at point C. If Ao = 5, OB = 12, the length of BC is obtained
15. As shown in the figure, OA, ob, OC are ⊙ o radius - AC = - BC, D, e are OA, ob, are the midpoint CD and CE equal? Why is it as shown in the figure
16. As shown in the figure, ⊙ o radius OA is the diameter of ⊙ O1, ⊙ o another radius OC intersection ⊙ O1 and point B, try to explain the arc length relationship between chord AB and chord AC
17. As shown in the figure, it is known that in △ AOB, ∠ AOB = 90 ° OD ⊥ AB is at point D. the circle with point o as the center and OD as the radius intersects OA at point E, intercept BC = ob on Ba, and prove that CE is the tangent of ⊙ o
18. As shown in the figure, in the two concentric circles with o as the center, the chord AB and CD of the big circle are equal, and AB and the small circle are tangent at point E
19. As shown in the figure, the center of two concentric circles is O, the radius of big circle O is OA, OB intersects small circle O with C, D, please explain: AB / / CD I hope we don't use center angle and circle angle
20. As shown in the figure, BD is the diameter of ⊙ o, OA ⊥ ob, M is the point on the inferior arc AB, through point m as the tangent of ⊙ o, the extension line of OA at point P, MD and OA at point n. (1) verification: PM = PN; (2) if BD = 4, PA = 32ao, through point B as BC ∥ MP intersection ⊙ o at point C, the length of BC