??? (1 Viewer)

[Sirius Black]

The point P lies on the circumference of a cirlcle of radius r and diameter AB. The point C lies on AB and PC is perpendicular to AB. The arc AP subtends an angle # at the centre O. The length of the arc AP is twice the length of the arc BP
Show that 2sin(#)=#

er... since lA^P=2 l P^B
<POB=#/2 (l=#r)
If this is right, then #=2pi/3, and the statement of 2sin(#)=# would be wrong
could any1 here help plz?

 

[Will Hunting]

No worries, dude.

AB is a diameter. Therefore, the arc, AB is half the circumference.

If the arc, AP is twice the length of the arc, AB, then AP is the circumference.

i.e. Point A is Point P

Hence, # = 2pi = 360&deg; = 0&deg; (From general, # = 180n, n integral)

Now, 2sin# = 2sin(2pi) = 2 x 0 = 0 = #

As to PC meeting AB for PC&perp;AB, it can be said that the point C is also point P which is also point A (since A, P and now C all lie on AB). If all three points are the same, then the interval joining any two of these points is at the same time perpendicular and parallel to any other interval joining any other two of the three points.

 

[Sirius Black]

!

sorry Will_Hunting i typed the wrong q but thanx all the same

 

[Sirius Black]

could any one help? thanx

 

[jumb]

could any one help? thanx

Will Hunting edited his post and has answered the new question.

 

[Sirius Black]

Will Hunting edited his post and has answered the new question.

he still assumed arc AP=2arc AB, rather than arc AP=2 arc BP

 

[illin]

ok got it

Draw a diagram, so much easier

LAPO = #
therefore LPOB = 180-#
POC is a triangle, and (180-#) + 90=180 (angle sum of a triangle)
therefore # = 90
therefore the point C in the centre of the circle O
I'll let u work from there, easy now

 

[Sirius Black]

ok got it

Draw a diagram, so much easier

LAPO = #
therefore LPOB = 180-#
POC is a triangle, and (180-#) + 90=180 (angle sum of a triangle)
therefore # = 90
therefore the point C in the centre of the circle O
I'll let u work from there, easy now

sorrie. i think ur anwer is incorrect coz # should be 120 if u drew the correct diagram and c is not the centre of the circle
Thanx for ur attempt anyway

 

[LaCe]

Yeah it looks like an obtuse angle, but i dont see any problem with the reasoning...
um...
wait u cant assume that POC is a triangle cause C can lie between A and O or O and B