In the triangle ABC, the angle ABC is the acute angle, the point D is the moving point on the ray BC, connecting ad, and making a square ADEF on the right side of ad with AD as one side If AB = AC and BAC = 90, is CF perpendicular to BD when point D is on the extension line of BC? If AB is not equal to AC angle, BAC is not equal to 90 point D, then BC motion triangle ABC satisfies what condition CF is perpendicular to BC If AC = 4, radical 2, BC = 3, under the condition of 2, let CF intersection of square ADEF and P find the maximum value of CP

In the triangle ABC, the angle ABC is the acute angle, the point D is the moving point on the ray BC, connecting ad, and making a square ADEF on the right side of ad with AD as one side If AB = AC and BAC = 90, is CF perpendicular to BD when point D is on the extension line of BC? If AB is not equal to AC angle, BAC is not equal to 90 point D, then BC motion triangle ABC satisfies what condition CF is perpendicular to BC If AC = 4, radical 2, BC = 3, under the condition of 2, let CF intersection of square ADEF and P find the maximum value of CP

(1) Yes,
From ab = AC, ad = AF, ∠ bad = 90 °+ ∠ CAD = ∠ CAF = 90 °+ ∠ CAD,
Determine △ bad ≌ △ CaF (SAS)
Therefore, ACF = abd,
Is CF vertical equal to BD
(2) It is known from (1) that an isosceles right triangle is needed,
Suppose that CF is perpendicular to BC when ABC satisfies the condition of ∠ ACB = 45 °
When ∠ ACB = 45 °, make the isosceles right triangle AOC, ∠ Cao = 90 °, o point is on the BC line, on the left side of C,
Similar to (1), it is proved that △ OAD ≌ △ CAF can deduce the vertical relationship;
(3) When AC = 4 * √ 2, BC = 3, ∠ ACB = 45 °, CF of square ADEF intersects P,
When d starts to move to the right from point B,
When D and C coincide, CP = 0,
Initial situation: D at point B, do not analyze first, draw a good picture and put it;
In the end case, P is at infinity, which is equivalent to AP / / BC. The maximum value of CP is the distance from C to CP, which is △ ABC
The length of the height on the side of BC is 4 * √ 2 * sin 45 ° = 4