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# Circles question .. watch

1. AB is a diameter of a circle and C is any point on the circumference of the circle. Then
a)area of ABC is maximum when it is isosceles.b)area of ABCis minimum when it is isosceles.c)perimeter of ABC is minimum when it is isoscelesd)none
2. (Original post by Carman3)
AB is a diameter of a circle and C is any point on the circumference of the circle. Then
a)area of ABC is maximum when it is isosceles.b)area of ABCis minimum when it is isosceles.c)perimeter of ABC is minimum when it is isoscelesd)none
3. the triangle is isosceles when C is at the highest point of the circle ?
4. So im writing this as im going along and this will only get u one mark (the answer)

so lets say the triangle is isoceles (spoiler it can be, put C at very top, put line between that and diameter, pythag/trig proves it can be isoceles)
now lets say the diameter is 5. we know isoceles triangles have the other two sides equal.
a^2+b^2=c^2
knowing these things i said we get
2a^2=5^2
solving gives 5/root2
If we then use the formula area=1/2 ab sinC
we get the area to be 6.25.
Now if we say a is 3 and b is 4 (not isocoles)
the area becomes 6. therefore we know option B is false.

In fact if you put any values for a and b you'll find they dont go higher than 6.25
therefore option A is correct.

(i got bored as i need to revise some crazy hard chemistry but i still wanted to help a bit)
5. (Original post by Toasticide)
So im writing this as im going along and this will only get u one mark (the answer)

so lets say the triangle is isoceles (spoiler it can be, put C at very top, put line between that and diameter, pythag/trig proves it can be isoceles)
now lets say the diameter is 5. we know isoceles triangles have the other two sides equal.
a^2+b^2=c^2
knowing these things i said we get
2a^2=5^2
solving gives 5/root2
If we then use the formula area=1/2 ab sinC
we get the area to be 6.25.
Now if we say a is 3 and b is 4 (not isocoles)
the area becomes 6. therefore we know option B is false.

In fact if you put any values for a and b you'll find they dont go higher than 6.25
therefore option A is correct.

(i got bored as i need to revise some crazy hard chemistry but i still wanted to help a bit)
Thanks.

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