Please use the following image for the next 7 questions. Keep in mind that because XY is tangent to circle M, XM and XM form a right angle.

Question

XM = 11 and YM = 36.

What is the area of circle M?
What is the circumference of circle M?
Find the length of XY .
Find the measure of angle M.
Find the area of triangle XYM.
Find the area of the minor sector that has been created as part of triangle XYM.
Find the arc length of the minor arc from point X to the point where YM intersects with the circle.

Answer 1

Because XY is a tangent, XM is a radius=11, so the area of the circle is π(11)²=121π. sq units.

YM²=XY²+XM², so 36²=XY²+11², 1296=XY²+121, XY²=1175, XY²=25×47, XY=5√47=34.28 units approx.

cosM=XM/YM=11/36, m∠M=72.21° approx. This is 1.2603 radians.

Area of ΔXYM=½XM.XY=½(11)(5√47)=27.5√47=188.53 sq units approx.

Area of ⌔XYM=½(11)²×1.2603=76.25 sq units approx. (Formula is A=½r²θ.)

Length of arc=11×1.2603=13.86 units approx. (Formula is s=rθ.)