I have solved for the area of quadrilateral but I don't know if that would help.
A = pi(r)^2
A = pi(d/2)^2
36pi = pi (d^2/4)
144 = d^2
12 = d
then solving for the quadrilateral's area
A = 1/2(8)(12)
A = 48 cm^2
but then I don't know what else to do.
Find the lengths of the sides of the cylcic quadrilateral if one diagonal coincides with a diameter of a circle whose area is 36pi cm squared. The other diagonal measures 8 cm meets the fist diagonal at right angles.
2 answers
Remember that in a cyclic quadrilateral, the diagonal subtends a 90° angle.
Since the two diagonals also intersect at 90°, the shorter diagonal must be bisected by the diameter.
In my diagram, I labeled the diameter A and B and the point on the circle above AB as C
My other diagonal meets AB at D and CD = 4
We now look at 3 similar triangles,
ABC is similar to ADC is similar to CBD
AB = 12 and CD = 4
you can set up ratios
give it a try
Since the two diagonals also intersect at 90°, the shorter diagonal must be bisected by the diameter.
In my diagram, I labeled the diameter A and B and the point on the circle above AB as C
My other diagonal meets AB at D and CD = 4
We now look at 3 similar triangles,
ABC is similar to ADC is similar to CBD
AB = 12 and CD = 4
you can set up ratios
give it a try
2 answers