SOLUTION: two distinct, nonparallel lines are tangent to a circle. the measurement of the angle between the two lines is 54 (angle QVP) a. Suppose the diameter of the circle is 2 cm. What

Question 59619: two distinct, nonparallel lines are tangent to a circle. the measurement of the angle between the two lines is 54 (angle QVP)
a. Suppose the diameter of the circle is 2 cm. What is the distance VP?
b. Suppose the distance VP is 3.93cm. What is the diameter of the circle?
c. Find a formula for d, the diameter of the circle, in terms of VP.
d. Find a formula for VP in terms of d, the diameter of the circle.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
two distinct, nonparallel lines are tangent to a circle. the measurement of the angle between the two lines is 54 (angle QVP)
a. Suppose the diameter of the circle is 2 cm. What is the distance VP?
b. Suppose the distance VP is 3.93cm. What is the diameter of the circle?
c. Find a formula for d, the diameter of the circle, in terms of VP.
d. Find a formula for VP in terms of d, the diameter of the circle.
HOPE YOU MEAN P & Q ARE ON THE CIRCLE AND VP AND VQ ARE TANGENTS
ASSUMING THAT,LET C BE CENTRE OF CIRCLE.THEN VCP IS A RIGHT ANGLED TRIANGLE.
ANGLE VPC=90
ANGLE PVC = ANGLE PVQ/2 = 54/2 =27
CP=D/2..WHERE D IS DIAMETER OF CIRCLE.
a. Suppose the diameter of the circle is 2 cm. What is the distance VP?
TAN(27)=CP/VP
CP=2/2=1
VP=1/TAN(27)=1.964
b. Suppose the distance VP is 3.93cm. What is the diameter of the circle?
TAN(27)=CP/3.93
DIAMETER =2*CP=2*3.93*TAN(27)= 4 CM
c. Find a formula for d, the diameter of the circle, in terms of VP.
D=2*VP*TAN(27)
d. Find a formula for VP in terms of d, the diameter of the circle.
VP = D/[2TAN(27)]
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