Cho hai đường tròn (O;R) và (O';r) cố định, tiếp xúc ngoài với nhau tại A (R>r). M là điểm thuộc đường tròn (O;R), N là điểm thuộc đường tròn (O';r) sao cho góc MAN= 90 độ a) Chứng minh OM // O'N
b) Chứng minh đường thẳng MN luôn đi qua một điểm cố định

a. she will receive a refund of $278.

step-by-step explanation:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.

i would say b) is your answer

sorry if im wrong

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: