Question

Hi I need help for the question below as attached related to Circle. Please help thanks!! The answer given in book is x=150, y=60

Answer 1

Just in case cannot see the questions clearly. It stated that the arcs QV and QW are of the same length. Determine values of x and y.

Answer 2

angle pvq is 90 coz it is a right triangle, so angle wvq is 75. WOQ is double of qvq is 150. I just got this but y i not sure how~

Answer 3

since QV and QW are the same..
then both of 75.
one quadrilateral is 360. so 360 - 75 - 15 - 210 = 60

my friends told me these but i still dun understand why P is 75

Answer 4

im horrible at drawing so im going to try to show this without drawing a diagram

ok if you extend the line OW through the circle to point R
then arc VR is 2y and arc of semi-circle is 180 degrees
you can set up this equation:
--> x+(x-2y) = 180
--> 2x-2y = 180
--> x -y = 90

also we know that arc PW is 30 thus angle WOP is 30
lets call the point where lines OP and WV cross "S"
the 3rd angle in triangle WOS can be defined as (150 -y)

angle VPQ is x/2
so using triangle VSP we can set up the following equation
--> (x/2) +15 + (150-y) = 180
--> (x/2) -y = 15
--> x -2y = 30

solve system of 2 equations to get x,y

Answer 5

I dun understand why arc VR is 2y

Answer 6

is it a formula if inside is y then the outside must be doubled of the inside??

Answer 7

if it is isosceles triangle then the two angles are same by definition and then u have