Find the measure of the arc or central angle indicated. Assume that the lines which’s appear to be diameters are actual diameters.

m∠HKF = 87°

Solution:

Given data:

m(ar JF) = 135° and m(ar GH) = 42°

GJ is the diameter of the circle.

Angle in a diameter is 180°.

⇒ m(ar JF) + m(ar FG) = 180°

⇒ 135° + m(ar FG) = 180°

Subtract 135° from both sides of the equation.

⇒ m(ar FG) = 45°

⇒ m(ar FGH) = m(ar FG) + m(ar GH)

⇒ m(ar FGH)= 45° + 42°

⇒ m(ar FGH) = 87°

The measure of the central angle is congruent to the measure of the intercepted arc.

⇒ m∠HKF = m(ar FGH)

⇒ m∠HKF = 87°

its a straight line parallel to the time axis

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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