给您一道初中8年级数学中平行四边形几何综合题,请您给我讲解,讲出这里显性和隐形的知识点,如果找到关键点,如何推导出所问问题的答案,因为有三个问题,请逐个帮我讲,谢谢---```text
Question 22. (13 points)
Common Setup: In △ABC, ∠C=90°, point M is a point on segment BC, connect AM.
Part (1):
Text: (1) As shown in Figure 1, AC=BC, AM is the angle bisector of △ABC, ME⊥AB at point E.
Question: When CM=4, find the length of AB;
Figure 1 Description:
Type: Geometric figure (triangle).
Main Elements:
- Triangle ABC with a right angle at vertex C (indicated by a square symbol).
- Point M is located on the side BC.
- Line segment AM is drawn.
- Point E is located on the side AB.
- Line segment ME is drawn, and it is perpendicular to AB at E (indicated by a right angle symbol at E).
- Labels: A, B, C, M, E.
Part (2):
Text: (2) If the median CO of △ABC intersects AM at point F, determine the relationship between CF and MF, and explain the reason;
Part (3) (Numbered as (2) in the original text):
Text: (2) As shown in Figure 2, if BM=AC, point N is a point on AC, and AN=CM, connect BN intersecting AM at point P, find the measure of ∠BPM.
Figure 2 Description:
Type: Geometric figure (triangle).
Main Elements:
- Triangle ABC with a right angle at vertex C (implied by being part of the same problem and no contradictory information, though not explicitly marked in this figure).
- Point M is located on the side BC.
- Point N is located on the side AC.
- Line segment AM is drawn.
- Line segment BN is drawn.
- Line segments AM and BN intersect at point P.
- Labels: A, B, C, M, N, P.
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