Posted by hii on Sunday, September 16, 2007 at 5:43pm.
HELP PLZZ...A circle has radius 2 cm,(in that circle there is a traingle ABO)
O is the centre of the circle.
the chord AB has length 3 cm. .
BO is 2cm
AO is 2cm
(i) Show that ÚAOB is 1.696 radians (to three decimal places).
(ii) Hence ﬁnd the area of the (smaller) sector AOB.
(iii) Find the area of the triangle AOB.
(iv) Hence ﬁnd the (smaller) area enclosed between the chord AB and the circle
(v) Express both the area of the sector and the area from part (a)(iv) as percentages of the area of the circle.
- can xome1 help me plzz im stuck - bobpursley, Sunday, September 16, 2007 at 5:49pm
draw a perpendicular from O to AB. Let x be the intersection. You know xb, and bo lengths, so find the sine of obx, thence the measure of obx. Double it to get boa.
The rest come from that.
Iwill be happy to critique your thinking.
- wod this be right? - hi, Monday, September 17, 2007 at 5:14pm
This splits the triangle into two right triangles, each with
hypotenuse 2, and adjacent side = 1.5
cos ¦È = adjacent / hypotenuse = (1.5) / 2 = 0.75
¦È = arccos (0.75) ¡Ö 0.723 radians
Angle(AOB) = ¦Ð - 2¦È ¡Ö ¦Ð - 1.446 ¡Ö 1.696 radians.
Area of one of the small right triangles is (1/2)bh
Need to find h (length of segment from 0 to midpt AB)
sin ¦È = opposite / hypotenuse
opposite = (hypotenuse) * sin ¦È = 2 * sin (0.723 radians)
¡Ö 1.323 cm
So area of one of the small right triangles
¡Ö (1/2) (1.5) (1.323) ¡Ö 0.992 cm^2
Area of triangle AOB is two times this amount or ¡Ö 1.984 cm^2
for v) area oc circle , pie r ^2 = pie 2^2 = 12.56
so 100 / 12.56 x 1.984 = 15.796 which is 15%
Answer This Question
More Related Questions
- maths - A chord is 2cm from the centre of a circle. if the ratius of the circle ...
- math - ) A chord AB of length 13cm is drawn in a circle centre O at a distance ...
- math - The equation of a circle with centre O(0,0) is x^2+y^2=40. The points A(-...
- Gss Giza , nasarawa state - Q.1.Calculate the length of an are of a circle of ...
- maths - Im confused can any1 help me on this question ?? or try and put me on ...
- math circle geometrics - The distance of a chord from the centre of a circle of ...
- math - Two chords in a circle are equal in lengh.The distances from the centre ...
- Maths - AB is a chord with centre O and radius 4 cm. AB is of length 4 cm and ...
- Mathematics - If a chord of length 10cm is at a distance of 12 cm from the ...
- Circle geometry - Please help Explain how I figure this out. A circle has ...