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not in order and may be incomplete ABC =180 -60 = 120 ACB = 180- (25 + 120) = 180 - 145 = 35 AC = BD BDC =25 given AD = 65 DA is perpendicular to AE 65 + 25 = 90 = DAB
@triciaal why AC=BD?
BC parallel to AD Chord BC similar figures ABC and DCB
How BC paralll to AC? impossible
do u have a screenshot? i cant open the document... :-/
for part (b), angle ADB is 1/2 arc AB which we know from part (a) for part (c), angle CAB= 65+25= 90 i.e. a right angle. if the inscribed angle is 90 degrees, then the chord is a diameter.
in general, use the the idea that inscribed angles that subtend the same arc are equal |dw:1439469998213:dw|
i) inscribed angle
for part (c), angle CAB= 65+25= 90 i.e. a right angle. if the inscribed angle is 90 degrees, then the chord is a diameter. //How CAB is 90 when it is 25
oops, I meant angle BAD is 90
from the picture, can you find the length (in degrees) of arc BC ?
okay BAD, yes
n I cant find arc BC, let me analyse...hmmm....
look for an inscribed angle that "opens" on arc BC
yes, but not useful. there is another one
yes, BAC also opens on arc BC. now we can figure out what arc BC is (it is 2 times angle BAC)
means 50? is there some theorem or axiom. can you tel me?
arc BC is 50?
next, we can find angle BCA . do you follow the reasoning?
BCA, can we find by 180-25-120=35.? cauz angle ABC is 120
I didn't get about the arc and angle relation. I know one thing theta=L/R But never tried this one
ok, but meanwhile you now know arc AB is what ?
yes. now we know arc AC 70+50= 120
and finally, we can find inscribed angle ADC (which opens on arc AC)
okay arc AC...
But please let me know the theorem. Send me some video link or something.... awesome....
Thank you @phi
ADB is 35? @phi