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12 votes
5. in the following figure, GE= r.

where ris the radius of the circle.
a) What is the nature of the triangle GEO? Justify your answer.
b) By calculating SEG in two different ways. using ares of the ​

5. in the following figure, GE= r. where ris the radius of the circle. a) What is-example-1
User Doxsi
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1 Answer

24 votes
24 votes

Answer + Step-by-step explanation:

a) GE = r = GM

Then GEO is an isosceles triangle

b) since GEO is an isosceles triangle then :

m∠SEG = m∠GOM = measure of the arc GM (mGM) (result 1)

On the other hand :

m∠SEG = m∠SEG = (1/2)×(mAS - mGM) (it’s a formula) (result 2)

Now ,we equate (result 1) and (result 2) :

m∠SEG = mGM

m∠SEG = (1/2)×(mAS - mGM)

Then

mGM = (1/2)×(mAS - mGM)

c) mGM = (1/2)×(mAS - mGM)

⇔ 2mGM = mAS - mGM

⇔ 3mGM = mAS

⇔ 3m∠SEA = m∠SOA

Remember:

mGM = m∠GOM = m∠SEA

User Tiagoams
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