In △ ABC, ∠ BAC = 90 °, BD bisection ∠ ABC, AE ⊥ BC in E. verification: AF = ad

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• 1. In △ ABC, ∠ BAC = 90 °, BD bisection ∠ ABC, AE ⊥ BC in E. verification: AF = ad
• 2. In triangle ABC, ad is high, be is middle line, angle CBE = 30 degrees, prove: ad = be
• 3. It is known that be is the middle line ad ⊥ BC in △ ABC, and it is shown that ad = be
• 4. In △ ABC, be is the middle line, ad ⊥ BC is in D, ∠ CBE = 30 °, please prove: ad = be The figure can be drawn according to the title. There are three sides of the triangle, one middle line and one high line. There are five sides in total
• 5. As shown in the figure, points a, B, D and E are on ⊙ o, and the extension lines of strings AE and BD intersect at point C. If AB is the diameter of ⊙ o, D is the midpoint of BC. Try to judge the size relationship between AB and AC, and give the proof Under the above conditions, what other conditions do △ ABC need to satisfy, and point e must be the midpoint of AC?
• 6. As shown in the figure, the tangent line AC passing through a point a on ⊙ O and the extension line of diameter BD of ⊙ o intersect at point C, and AE ⊥ BC passing through a intersects at point E. (1) prove: ∠ CAE = 2 ∠ B; (2) know: AC = 8 and CD = 4, find the radius of ⊙ O and the length of AE
• 7. As shown in the figure, BD is the diameter of circle O, e is a point on circle O, the straight line AE intersects the extension line of BD at point a, BC ⊥ AE at point C, and ∠ CBE = ∠ DBE. (1) try to explain that AC is the tangent line of circle O. (2) if the radius of circle O is 2, AE = 4, root 2, find the length of de
• 8. As shown in the figure, points a, B, D and E are on ⊙ o, and the extension lines of strings AE and BD intersect at point C. If AB is the diameter of ⊙ o, D is the midpoint of BC. Try to judge the size relationship between AB and AC, and give the proof
• 9. The point ABCDE is on the circle O, and the extension lines of the strings AE and BD are compared with the point C. AB is the diameter of the circle and D is the midpoint of BC Judge the size relationship between AB and AC What conditions should triangle ABC satisfy? Point e must be the midpoint of AC
• 10. As shown in the figure, BC is the diameter of circle O, a is a point on circle O, cross point C to make the tangent line of circle O, intersect the extension line of BA at point D, and take the midpoint e of CD, the extension line of AE and the tangent line of BC (1) prove that AP is the tangent of circle O. (2) if OC = CP, ab = 3 √ 3, find the length of CD
• 11. In △ ABC, a-c = 90 ° AE is the bisector of BAC, and the degree of AEC is calculated
• 12. As shown in the figure, in △ ABC, ad is the height of BC, AE is divided equally into ∠ BAC, ∠ B = 75, ∠ C = 45, and ∠ Daewoo and ∠ AEC are calculated
• 13. It is known that ad is the angular bisector of △ ABC, de ∥ AC intersects AB at point E, DF ∥ AB intersects AC at point F
• 14. It is known that ad is the angular bisector of △ ABC, de ∥ AC intersects AB at point E, DF ∥ AB intersects AC at point F
• 15. It is known that, as shown in the figure, ad is the angular bisector of △ ABC, and EF bisectors ad vertically, intersecting AB and AC at e and f respectively
• 16. As shown in the figure, in RT △ ABC, ∠ B = 90 °, a = 30 ° and AC = 3, bend BC toward Ba, so that point C falls on point C 'on Ba, and the crease is be, then the length of C' e is___ ．
• 17. As shown in the figure, in △ ABC, point P moves from point B along the Ba edge to point a at a speed of 1cm / s, and point Q also moves from point B along the BC edge to point C at a speed of 2cm / s. After a few seconds, the area of △ PBQ is 36cm2?
• 18. As shown in the figure, in the RT triangle ABC, ∠ C = 90, AC = 6cm, BC = 8cm, points E and f start from two points a and B at the same time and move to points c and B along the direction of AC and Ba respectively The velocity of point E is 2cm / s, and that of point F is 1cm / s. if one of the points reaches the position, both points stop moving (1) Q. after a few seconds, the area of the triangle AEF is 16 / 5 (2) After a few seconds, EF bisects the perimeter of the RT triangle (3) Is there a line EF that bisects the perimeter and area of rtabc at the same time? If so, calculate the length of AE. If not, explain the reason
• 19. As shown in the figure, in the RT triangle ABC & nbsp;, the angle c = 90 °, AC = 3, BC = 4, a straight line & nbsp; l intersects with the edge BC and Ba and points & nbsp; E and f respectively, and the area of the divided triangle ABC & nbsp; is two equal parts, then the minimum length of the segment EF & nbsp; is______ ．
• 20. As shown in the figure, in RT △ ABC, ∠ ABC is a right angle, ab = 3, BC = 4, P is the moving point on the edge of BC, let BP = x, if we can find a point Q on the edge of AC, so that ∠ BQP = 90 °, then the value range of X is______ ．