1.Show that the points (5,5),(6,4),(-2,4) and (7,1) are concyclic .Also find the equation ,centre and radius of the circle on wh
2 answers:
Answer:
- See below
Step-by-step explanation:
<em>This is how I solved it.</em>
Plotted the given points. See the attached.
<u>Identified two pairs to connect, the two chords.</u>
- (5. 5) with (7, 1) and (6,4) with (-2, 4).
<u>Determined the equation of both lines:</u>
- y -5 = [( 1 - 5)/(7-5)](x - 5) ⇒
- y - 5 = -2(x - 5)
- y = -2x + 15
and
- y = 4 (horizontal line)
Identified perpendicular bisectors of those two chords, they both pass through the center of circle.
<u>Midpoints of the chords:</u>
- [(5 + 7)/2, (5 + 1)/2] = (6, 3)
and
- (6 - 2)/ 2 = 2
<u>The equations:</u>
- y - 3 = 1/2(x - 6) ⇒ y = 1/2x
- x = 2 (perpendicular to y = 4 and passing through x = 2)
Solving the system found the intersecting of those, the center.
<u>Found the center: </u>
- (2, 1)
<u>Found the distance from the center to one of the points (7, 1):</u>
- 7 - 2 = 5, this is the radius
<u>The equation of circle:</u>
- (x - 2)² + (y - 1)² = 25
Verified all the other points are on same circle, confirmed.
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