Question

The length of AB chord of a circle is 36 meters.ACB is a circular arc located on the same side of the circle.The length of the ACB arc is 40 meters. The distance between center of the AB chord and C is 6 meters. What is the radius of the circle? explain it please​

Answer 1

First, let’s add 1 on both sides of the equality, so that we obtain:

xyz+xy+xz+yz+x+y+z+1=1001;

Secondly, group the terms as follows:

(xyz+yz)+(xy+y)+(xz+z)+(x+1)=1001.

Then, factor the groups:

yz(x+1)+y(x+1)+z(x+1)+(x+1)=1001,

where we observe that (x+1) is a common factor for all of the terms:

(x+1)(yz+y+z+1)=1001;

The second parentheses the terms can be also grouped as follows:

(x+1)((yz+y)+(z+1))=1001,

so that we obtain:

(x+1)(y+1)(z+1)=1001.

Knowing that x, y and z are natural numbers, we look for the possible factors of 1001:

They are: 1, 7, 11, 13, 77, 91, 143 and 1001.

So, 1001 can be decomposed as a product of three factors as follows:

1*1*1001, or 1*7*143, or 1*11*91, or 1*13*77, or 7*11*13,

The three factors product (x+1)(y+1)(z+1) is the same with any of the above cases. Taking the

cases one by one

(x+1=1, so x=0, y+1=1, so y=0, z+1=1001, so z=1000, etc.)

we obtain the triplet (x,y,z) of the forms:

(0,0,1000), (0,6,142), (0,10,90), (0,12,76), (6,10,12),

5 in total. Applying the circular permutations, we obtain 15 in fact (x=0, y=0, z=1000 or x=0,

y=1000, z=0, or x=1000, y=0, z=0, etc.).

Answer 2

Step-by-step explanation:

The length of AB chord of a circle is 36 meters.ACB is a circular arc located on the same side of the circle.The length of the ACB arc is 40 meters. The distance between center of the AB chord and C is 6 meters. What is the radius of the circle? explain it please