NoraNeko Reviewer
Theorem 3.4
If a secant and a tangent intersect on a circle then the measure of each angle formed is equal to half of the measure of its intercepted arc.
To find the measure of the angle, you will divide the actual given measure of the arc.
To find the measure of another angle, subtract 360 to the given arc. The final answer is divided by two.
You can form angles with a secant and a tangent. It usually takes up to 2 angles form.
This is for inscribed angle only.
Theorem 3.5
If two chords intersects then the measure of the angle formed is half the sum of the measures of the two arcs intercepted by the angle and its vertical angle.
To find the measure of the angle, you have to add the arc of the certain angle with the vertical angle, divide it by two.
Formula (Sample)::
m<1= (Arc) AD + (Arc) BC
--------------------------
2
To determine the measure of the vertical angle, it is equal to the angle it is vertical with or facing because of the vertical angle theorem.
If the two certain vertical arc isn’t equal, add up the vertical arc then divide it by two.
This is for chord only.
Theorem 3.6
If two secants, a secant and a tangent, or two tangents intersects outside a circle then the measure of the angle formed is equal to half the difference of the measures of its intercepted.
Intersection is outside the circle.
To find the measure of the angle, subtract the major arc and minor arc (intercepted arc) and divide by two.