Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. 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
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.