- arindameducationusc

This question was asked by m friend Sopie.
I am not able to solve it. Can anyone help?
See attachment

- chestercat

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- arindameducationusc

##### 1 Attachment

- 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

@triciaal why AC=BD?

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- triciaal

BC parallel to AD Chord BC
similar figures ABC and DCB

- arindameducationusc

How BC paralll to AC? impossible

- arindameducationusc

- Jack1

do u have a screenshot? i cant open the document... :-/

- phi

there are a few ways to find angle ADC. one way:
i)

##### 1 Attachment

- 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

in general, use the the idea that inscribed angles that subtend the same arc are equal
|dw:1439469998213:dw|

- arindameducationusc

i) inscribed angle

- 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

oops, I meant angle BAD is 90

- phi

from the picture, can you find the length (in degrees) of arc BC ?

- arindameducationusc

okay BAD, yes

- phi

|dw:1439470438536:dw|

- arindameducationusc

n I cant find arc BC, let me analyse...hmmm....

- phi

look for an inscribed angle that "opens" on arc BC

- arindameducationusc

angle BDC?

- phi

yes, but not useful. there is another one

- arindameducationusc

angle BAC?

- phi

yes, BAC also opens on arc BC. now we can figure out what arc BC is
(it is 2 times angle BAC)

- arindameducationusc

means 50?
is there some theorem or axiom. can you tel me?

- arindameducationusc

arc BC is 50?

- phi

yes

- phi

next, we can find angle BCA . do you follow the reasoning?

- arindameducationusc

BCA, can we find by 180-25-120=35.?
cauz angle ABC is 120

- phi

yes.

- arindameducationusc

I didn't get about the arc and angle relation.
I know one thing theta=L/R
But never tried this one

- phi

ok, but meanwhile you now know arc AB is what ?

- arindameducationusc

2*35=70

- arindameducationusc

right?

- phi

yes. now we know arc AC
70+50= 120

- phi

and finally, we can find inscribed angle ADC (which opens on arc AC)

- arindameducationusc

okay arc AC...

- arindameducationusc

60?

- phi

yes

- arindameducationusc

wow..!!

- arindameducationusc

But please let me know the theorem. Send me some video link or something.... awesome....

- phi

https://www.khanacademy.org/math/geometry/cc-geometry-circles/central-inscribed-circumscribed/v/inscribed-and-central-angles

- arindameducationusc

Thank you @phi

- arindameducationusc

ADB is 35? @phi

- phi

yes, both

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