As shown in the figure, AB is the diameter of ⊙ o, Pb is tangent to ⊙ o at point B, the extension line of chord AC ∥ OP and PC intersects BA at point D, proving that PD is tangent to ⊙ o

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• 1. AB is the diameter of the circle O, Pb tangents the circle O to B, D on the circle O, ad ‖ Po, prove that PD is the tangent of the circle o
• 2. It is known that: as shown in the figure, △ ABC is the inscribed triangle of O, the bisector of angle ACB intersects circle O at point D, and makes tangent l of circle O through point D. prove that AB is parallel to L
• 3. It is known that: as shown in the figure, △ ABC is the inscribed triangle of ⊙ o, ⊙ O's diameter BD intersects AC at e, AF ⊥ BD at F, extending AF intersects BC at g. the proof is AB2 = BG · BC
• 4. It is known that △ ABC is inscribed in ⊙ o, and ab is the diameter of ⊙ O. the bisector of ∠ ACB intersects ⊙ o at point D. if AB = 2cm, then ad=______ cm．
• 5. If P is a point outside the plane where △ ABC is located and the lines AP, BP and CP are perpendicular, then the projection of P on plane ABC is ()
• 6. As shown in the figure, D is any point on the bottom edge BC of the isosceles triangle ABC, take a point E, AE = ad on the ray AC, and verify the angle bad = 2 EDC
• 7. It is known that: as shown in the figure, in △ ABC, ∠ BAC = 120 ° AB = AC, the vertical bisector on the side of AB intersects BC at point D, intersects AB at point E, and connects ad, Verification: CD = 2bd
• 8. As shown in the figure, in the isosceles △ ABC, ab = AC, ∠ BAC = 120 °, ad is the height on the edge of BC, passing through point d to make de ‖ AB, intersecting AC at point E. in addition to △ ABC, is there any isosceles triangle in the figure? If yes, please point out and give reasons
• 9. Ready to leave after dinner?
• 10. Calculation: 19492-19502 + 19512-19522 + +19972-19982+19992=______ ．
• 11. EA is the tangent line of circle O, a is the tangent point, the chord BC intersects OA at D, through B makes Pb, vertical CB intersects EA extension line at P
• 12. In the eighth grade mathematics equilateral triangle ABC, there is a point P, AP is equal to 3, BP is equal to 1, CP is equal to 5?
• 13. As shown in the figure, given that points B, C and D are on the same straight line, △ ABC and △ CDE are equilateral triangles. Be intersects AC at F, ad intersects CE at h. ① verify: △ BCE ≌ △ ACD; ② verify: CF = ch; ③ judge the shape of △ CFH and explain the reason
• 14. Mathematics problems in grade two of junior high school (equilateral triangle) In △ ABC, ab = AC, ∠ BAC = 120 °, the vertical bisector of AB intersects BC at E. prove: be = half CE
• 15. As shown in the figure, BD is the height on the side of equilateral △ ABC, extend BC to e, so that CE = CD, (1) try to compare the size relationship between BD and De, and explain the reason; (2) if BD is changed to the angular bisector or median line of △ ABC, can we draw the same conclusion?
• 16. As shown in the figure, it is known that triangle ABC is an equilateral triangle, point P is any point on BC, and triangle AQP is also an equilateral triangle. Prove that triangle AQB ≌ triangle APC
• 17. As shown in the figure, it is known that in the triangle ABC, ab = AC, ad is the height on the edge of BC, and point P is in the triangle abd
• 18. It is known that △ ABC is an equilateral triangle, P is a point in the triangle, PA = 3, Pb = 4, PC = 5
• 19. It is known that △ ABC is an equilateral triangle, P is a point in the triangle, PA = 3, Pb = 4, PC = 5
• 20. P is a point in the equilateral triangle ABC, PC = 5, PA = 3, Pb = 4, find the degree of angle APB There are only four points a, P, B, C