Kite ABCD is inscribed in circle O such that BD = 12 and AE = 4.

(a) Determine the length of CE.

(b) Determine the perimeter of ABCD to the nearest tenth.

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a) CE = 9

b) Perimeter = 36.1

Step-by-step explanation:

a)

Using the property of chords in a circle, we have that:

DE * BE = AE * CE

As the diameter is perpendicular to the chord, the diameter cuts the chord in half, so BE = DE = BD/2 = 6

So we have that:

6 * 6 = 4 * CE

4 * CE = 36

CE = 9

b)

As the triangle BCE is congruent to the triangle DCE (using side-angle-side case), we have that BC = CD, and we can find them using Pythagoras' theorem in the triangle BCE:

BC^2 = DE^2 + EC^2

BC^2 = 6^2 = 9^2

BC^2 = 36 + 81 = 117

BC = 10.8167

As the triangle BAE is congruent to the triangle DAE (using side-angle-side case), we have that AB = AD, and we can find them using Pythagoras' theorem in the triangle BAE:

AB^2 = AE^2 + BE^2

AB^2 = 4^2 = 6^2

AB^2 = 16 + 36 = 52

AB = 7.2111

So the perimeter of ABCD is:

10.8167 + 10.8167 + 7.2111 + 7.2111 = 36.0556

Rounding to the nearest tenth, the perimeter is 36.1

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.