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"Circle Through Three Points" PPT courseware
1. A circle is _________ at three points that are not at _______________.
2. A circle can be drawn through the three vertices of a triangle. This circle is called the ________ of the triangle. The center of the circumscribed circle is called the ________ of the triangle.
3. The distance from the circumcenter of the triangle to the _________ of the triangle is equal.
1. (4 points) Through two points M and N, a ________ circle can be drawn, with the center of the circle at _______________.
2. (4 points) As shown in the figure, points A, B, and C are on the same straight line, and point M is outside AC. If a circle is drawn through the three points in the figure, _________ can be drawn.
3. (4 points) Which of the following conditions cannot determine a circle ()
A． Center and radius of circle B. diameter
C. The three vertices of the triangle D. Three known points on the plane
4. (4 points) According to the following conditions, the three points A, B, and C can determine a circle ()
A． AB=2, BC=2, AC=4
B． AB=4.5, BC=5.5, AC=10
C. AB=4, BC=3, AC=5
D. AB＝√2-1, BC＝√2+1, AC＝2√2
16． (10 points) Given the straight line l: y=x+4 and points A (0, 4), B (-4, 0), let point C be a point on the straight line l, determine whether A, B, C are on the same circle ．
When x=0, y=4, that is, point A is on the straight line l, similarly point B is also on the straight line l, and point C is on the straight line l, that is, A, B, and C are on the same straight line, so A, B , C is not on the same circle
17． (12 points) Restore the broken wheel in the picture. Three points A, B, and C on the arc are known.
(1) Draw the center of the circle;
(2) If △ABC is an isosceles triangle, base BC=16 cm, waist AB=10 cm, find the radius R of the disc.
(1) Draw the perpendicular bisectors of chords AB and AC respectively, and their intersection points are the center points of the wheel.
(2) Suppose the intersection point of AO and BC in ⊙O is D. From the property of three lines of an isosceles triangle uniting into one, we can get AD⊥BC. From the Pythagorean theorem, we can get R=25/3 cm
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"Circle Through Three Points" PPT Courseware 2:
"Circle Through Three Points" PPT Courseware 2 Thinking: An archaeologist found a incomplete funerary tile in an ancient tomb (according to records, the original shape was round), as shown in the picture, can you help him restore it to its original shape? shape? Study 1 How many circles can you draw through a point in the plane?