Describe the relationship between the segments made when secant lines intersect outside a circle. Use the following image as ref
erence.
1 answer:
Let the extensions of secants AD and BC meet at point P.
Let the measure of ar DC be 2a, then m(DAC)=m(DBC)=a, since angles DAC and DBC are both inscribed angles intercepting arc DC.
m(P)=b.
Then triangles APC and BPD are similar, because they have 2 pairs of common angles.
from the similarity of APC and BPD, we can write the ratios:
Let the measure of ar DC be 2a, then m(DAC)=m(DBC)=a, since angles DAC and DBC are both inscribed angles intercepting arc DC.
m(P)=b.
Then triangles APC and BPD are similar, because they have 2 pairs of common angles.
from the similarity of APC and BPD, we can write the ratios:
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100 × 0.2045454545 = 20.45454545
Now we need to subtract our original number.
Now we put that over 99 (that's one less than our 100 from earlier)
Our fraction is shaping up, but we shouldn't have a decimal in there. Let's multiply the top and bottom by 100 to get rid of it.
We're going to have to do some simplifying. (the top and bottom are both clearly divisible by 5 and then some)
<em> done!</em>
100 × 0.2045454545 = 20.45454545
Now we need to subtract our original number.
Now we put that over 99 (that's one less than our 100 from earlier)
Our fraction is shaping up, but we shouldn't have a decimal in there. Let's multiply the top and bottom by 100 to get rid of it.
We're going to have to do some simplifying. (the top and bottom are both clearly divisible by 5 and then some)