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Author Topic: How to solve these types of questions ??  (Read 1870 times)

Offline d0ckn3ss

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How to solve these types of questions ??
« on: October 11, 2011, 03:49:38 pm »
hi guys... i would like to know how to solve these types of equations

Lets say we have a sector of a circle OAB ( O is the origin)  


Radius is 6
Theta= Pie/3

Tangent of Point A and and tangent of point B meet at point X

1) find the length of AX
2) find the area of AXB

now i know that the length arc is r(theta) and area of sector is 1/2(r)^2(theta)
but how do i find out what AX is and the area of AXB ?

and i also attatched another question that is similar
« Last Edit: October 11, 2011, 03:53:12 pm by d0ckn3ss »
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Offline Arthur Bon Zavi

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Re: How to solve these types of questions ??
« Reply #1 on: October 11, 2011, 05:45:01 pm »
Solving the attachment.

(5) (i)

OA = OB

(AB)2 = (OA)2 + (OB)2
(AB)2 = (6)2 + (6)2
(AB)2 = 36 + 36
(AB)2 = 72
AB = \sqrt 72

AB = OD

angle BAD : tan \theta = (\frac{opposite}{adjacent})

tan \theta =  6/6
\theta = tan-1 (6/6)
\theta = 45o or (\frac{45}{180})\pi = (\frac{1}{4})\pi

length of arc : s = r X \theta
                                = \sqrt 72 X (\frac{1}{4})\pi
                                = 6.664324407 or 6.67 (correct to 3 significant figures)

(ii)

Area of shaded region = Area of sector ABD - Area of triangle AOB
Area of shaded region = [ (\frac{1}{2})r^2 X \theta ] - [ (\frac{1}{2}) X b X h] ]
Area of shaded region = [ (\frac{1}{2}) X 72 X (\frac{1}{4} \pi) ] - [ (\frac{1}{2}) X 6 X 6]
Area of shaded region = 9\pi - 18
Area of shaded region = 9 (\pi - 2) = 10.2743338 or 10.3 (correct to 3 significant figures)
« Last Edit: October 11, 2011, 06:06:05 pm by Arthur Bon Zavi »
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Offline Arthur Bon Zavi

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Re: How to solve these types of questions ??
« Reply #2 on: October 11, 2011, 06:12:19 pm »
Quote from: d0ckn3ss on October 11, 2011, 03:49:38 pm
Tangent of Point A and and tangent of point B meet at point X

This part is not clear. The tangent can be from any direction and be of any length.
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Offline d0ckn3ss

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Re: How to solve these types of questions ??
« Reply #3 on: October 12, 2011, 01:26:16 am »
maybee this can help you understand

attached a file
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