Can anybody answer and explain this question
Answers
Answer:
sorry I can't explain this question
Answer:
4√3
Step-by-step explanation:
Chords AB and CD of a circle intersect at E and are perpendicular to each other. Segments AE, EB and ED have a length of 2cm , 6cm and 3 cm respectively. What is the length of diameter of a circle in cm?
Chords AB and CD of a circle intersect at E and are perpendicular to each other. Segments AE, EB and ED have a length of 2 cm 6 cm and 3 cm, respectively. What is the length of diameter of a circle in cm?
Since the the two chords AB and CD intersect at E, AE * EB = CE * ED. So
2 * 6 = 3 * EC, or
EC = 2 * 6/3 = 4 cm.
So the chord CD = EC + ED =4+3 = 7 cm and AB = AE+EB = 2+6 = 8 cm
Let OM be a perpendicular from the center, O on AB and let ON be a perpendicular from the center, O on CD.
EM = (2+6)/2 - AE = 4–2 = 2 cm
EN = 4 -(4+3)/2 = 0.5 cm
OE = [2^2 + 0.5^2]^0.5 = 4.25^0.5 = 2.061552813 cm.
Let R be the radius of the circle. Let EO extended meet the circumference at S and T. TE = R-OE or (R - 2.061552813) and ES = R + OE = (R + 2.061552813)
TE * ES = AE * EB
(R - 2.061552813)*(R + 2.061552813) = 2*6 = 12
R^2 - 2.061552813^2 = 12, or
R^2 = 12 +2.061552813^2 = 16.25
So R = 16.25^(0.5) = 4.031128874 cm
The radius of the circle is 4.031128874 cm.