A circle touches the y axis at point 0,4 and cuts x axis a cord of 6 ubits, then radius of circle is
Answers
Firstly:
A) The circle touches the Y−Axis in A(0,3), which means thatY−Axis is a tangent line to it at A, yields that E is located in a line parallel to Y−Axis and passing through A
B) That the circle intersects thex−axis in (8,0), means either:
1) the point C has (0,8) as coordinates.
2) or The point B is the one that is located at those coordinates .
The first case is rejected by the first condition, meanwhile the second one is accepted.
So according to the figure above, in the right triangle EDB, we find that:
ED2+DB2=EB2it means that 32+(8−R)2=R2 , it yields that R=7316
Then the coordinates of E are (R=7316,3)
Hence, the equation of the circle is:
(x−7316)2+(y−3)2=732162
Answer:
Step-by-step explanation:
As the circle cuts the x-axis in a chord of length 6 units, so,
AC=CB=3
In ΔAPC, by Pythagoras theorem,
(AP)^2 =(PC)^2+(AC)^2
r^2 = 3^2 + 4^2
r=5
Therefore, the radius of the circle is 5 cm.