Math, asked by nightfury81, 5 months ago

Can anybody answer and explain this question

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Answered by pandasontosh696
1

Answer:

sorry I can't explain this question

Answered by Anonymous
2

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.

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