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There is a (0,1) B (2,1) C (3,4) d (2,4) 1 in the plane rectangular coordinate system There is a (0,1) B (2,1) C (3,4) d (2,4) 1 in the plane rectangular coordinate system. 2. If the midpoint of the chord cut by the circle m is exactly the point D, the equation of the straight line is obtained
1. Circle radius r = AP = BP = CP, from a (0,1), B (2,1), we can know that the center of the circle is (1, y), (1-0) ^ 2 + (Y-1) ^ 2 = (3-1) ^ 2 + (4-y) ^ 2, we can get y = 3, the center of the circle is (1,3). Then r = 5, the circle equation is (x-1) ^ 2 + (Y-3) ^ 2 = 52, (2,4) is the midpoint of the chord, then the slope of the straight line is - 1, y = - x + B, the midpoint of the chord is on the straight line
In △ ABC, ∠ A is 90 °, AC = AB, P is a point in △ ABC, PA = 1, Pb = 3, PC = √ 7. Find the size of ∠ APC
Rotate △ APC 90 degrees around point a to make C turn to B, and then set p to Q
AQ=AP=1,BQ=PC=√7,∠PAQ=90°.
Δ PAQ is isosceles right triangle, PQ = √ 2, ∠ AQP = 45 °
PQ ^ 2 = 2, QB ^ 2 = 7, Pb ^ 2 = 9, satisfying PQ ^ 2 + QB ^ 2 = Pb ^ 2, so △ bpq is a right triangle, ∠ pqb = 90 °
∠CPA=∠BQA=∠PQB+∠AQP=45°+90°=135°.
In RT △ ABC, ∠ a = 90 ° BC = 4, there is an internal angle of 60 ° and the point P is different on the straight line ab
The test points of this problem are: right triangle with 30 degree angle; Pythagorean theorem
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