arindameducationusc
  • arindameducationusc
This question was asked by m friend Sopie. I am not able to solve it. Can anyone help? See attachment
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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arindameducationusc
  • arindameducationusc
1 Attachment
triciaal
  • triciaal
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
arindameducationusc
  • arindameducationusc
@triciaal why AC=BD?

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triciaal
  • triciaal
BC parallel to AD Chord BC similar figures ABC and DCB
arindameducationusc
  • arindameducationusc
How BC paralll to AC? impossible
arindameducationusc
  • arindameducationusc
@triciaal
Jack1
  • Jack1
do u have a screenshot? i cant open the document... :-/
phi
  • phi
there are a few ways to find angle ADC. one way: i)
phi
  • phi
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.
phi
  • phi
in general, use the the idea that inscribed angles that subtend the same arc are equal |dw:1439469998213:dw|
arindameducationusc
  • arindameducationusc
i) inscribed angle
arindameducationusc
  • arindameducationusc
@phi
arindameducationusc
  • arindameducationusc
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
phi
  • phi
oops, I meant angle BAD is 90
phi
  • phi
from the picture, can you find the length (in degrees) of arc BC ?
arindameducationusc
  • arindameducationusc
okay BAD, yes
phi
  • phi
|dw:1439470438536:dw|
arindameducationusc
  • arindameducationusc
n I cant find arc BC, let me analyse...hmmm....
phi
  • phi
look for an inscribed angle that "opens" on arc BC
arindameducationusc
  • arindameducationusc
angle BDC?
phi
  • phi
yes, but not useful. there is another one
arindameducationusc
  • arindameducationusc
angle BAC?
phi
  • phi
yes, BAC also opens on arc BC. now we can figure out what arc BC is (it is 2 times angle BAC)
arindameducationusc
  • arindameducationusc
means 50? is there some theorem or axiom. can you tel me?
arindameducationusc
  • arindameducationusc
arc BC is 50?
phi
  • phi
yes
phi
  • phi
next, we can find angle BCA . do you follow the reasoning?
arindameducationusc
  • arindameducationusc
BCA, can we find by 180-25-120=35.? cauz angle ABC is 120
phi
  • phi
yes.
arindameducationusc
  • arindameducationusc
I didn't get about the arc and angle relation. I know one thing theta=L/R But never tried this one
phi
  • phi
ok, but meanwhile you now know arc AB is what ?
arindameducationusc
  • arindameducationusc
2*35=70
arindameducationusc
  • arindameducationusc
right?
phi
  • phi
yes. now we know arc AC 70+50= 120
phi
  • phi
and finally, we can find inscribed angle ADC (which opens on arc AC)
arindameducationusc
  • arindameducationusc
okay arc AC...
arindameducationusc
  • arindameducationusc
60?
phi
  • phi
yes
arindameducationusc
  • arindameducationusc
wow..!!
arindameducationusc
  • arindameducationusc
But please let me know the theorem. Send me some video link or something.... awesome....
phi
  • phi
https://www.khanacademy.org/math/geometry/cc-geometry-circles/central-inscribed-circumscribed/v/inscribed-and-central-angles
arindameducationusc
  • arindameducationusc
Thank you @phi
arindameducationusc
  • arindameducationusc
ADB is 35? @phi
phi
  • phi
yes, both

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