Working With Circle Q

[nycmathguy]

 

[MathLover1]

given:
ST=1/2 (SR)
SR=a (diameter)
hint: draw QT

=>ST=1/2 (a)=a/2 (radius)
then we know that SQ=a/2 and QT=a/2
=> triangle SQT is an equilateral triangle, so all angles are equal and each measures 45°

a. m (ST)

Length of the arc (ST)= 2πr(theta/360°)

in your case r=a/2

(ST)=2π(a/2)(45°/360°)

(ST)=(2r*π)/8=(r*π)/4

(ST)=(a*π/2)/4

(ST)=(a*π)/8

b. m (TR)=circumference/2-ST= 2π-(a*π)/8=π (16 - a)/8

c. m (STR)=circumference/2 =(2(a/2)π)/2=(aπ)/2

answers:

a. m (ST)= (a*π)/8
b. m (TR)=π (16 - a)/8
c. m (STR)=(aπ)/2
d. m (S)= 45°

 

[nycmathguy]

given:
ST=1/2 (SR)
SR=a (diameter)
hint: draw QT

=>ST=1/2 (a)=a/2 (radius)
then we know that SQ=a/2 and QT=a/2
=> triangle SQT is an equilateral triangle, so all angles are equal and each measures 45°

a. m (ST)

Length of the arc (ST)= 2πr(theta/360°)

in your case r=a/2

(ST)=2π(a/2)(45°/360°)

(ST)=(2r*π)/8=(r*π)/4

(ST)=(a*π/2)/4

(ST)=(a*π)/8

b. m (TR)=circumference/2-ST= 2π-(a*π)/8=π (16 - a)/8

c. m (STR)=circumference/2 =(2(a/2)π)/2=(aπ)/2

answers:

a. m (ST)= (a*π)/8
b. m (TR)=π (16 - a)/8
c. m (STR)=(aπ)/2
d. m (S)= 45°

I know we are not studying geometry now. I just wanted to know how much of this material you are familiar with. I definitely will study geometry in a much deeper sense of the word in the near future.

 

[MathLover1]

did you forgot that I am math teacher

 

[nycmathguy]

did you forgot that I am math teacher

You were a math teacher but now you are retired. How do you keep yourself from forgetting this stuff taught years ago?

 

[MathLover1]

a math teacher does not forget everything when retires

 

[nycmathguy]

a math teacher does not forget everything when retires

Read what I said about Soroban and MarkFL.

 

[MathLover1]

who are they?

 

[nycmathguy]

who are they?

Two great guys from other forums. Now, I last heard from Soroban in 2006. He was 75 years old at the time. Can we say Soroban is no longer with us?
MarkFL ended contact with me a few years ago. He hates God as much as you do. In fact, Mark does not believe there is a God or an afterlife.