Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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 which they lie.​

Sagot :

mhanifa

Answer:

  • See below

Step-by-step explanation:

This is how I solved it.

Plotted the given points. See the attached.

Identified two pairs to connect, the two chords.

  • (5. 5) with (7, 1) and (6,4) with (-2, 4).

Determined the equation of both lines:

  • 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.

Midpoints of the chords:

  • [(5 + 7)/2, (5 + 1)/2] = (6, 3)

and

  • (6 - 2)/ 2 = 2

The equations:

  • 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.

Found the center:

  • (2, 1)

Found the distance from the center to one of the points (7, 1):

  • 7 - 2 = 5, this is the radius

The equation of circle:

  • (x - 2)² + (y - 1)² = 25

Verified all the other points are on same circle, confirmed.

View image mhanifa
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.