Question

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

Answer 1

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

Answer 2

@triciaal why AC=BD?

Answer 3

BC parallel to AD Chord BC
similar figures ABC and DCB

Answer 4

How BC paralll to AC? impossible

Answer 5

@triciaal

Answer 6

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

Answer 7

there are a few ways to find angle ADC. one way:
i) <CBE is an exterior angle of triangle ABC, so it equals the sum of the "opposite" angles:
<CBE= <BAC + <BCA
60 = 25 + <BCA
so
<BCA= 60-25= 35

ii) inscribed angle <ACD = 1/2 arc BC + 1/2 arc AB

from part i) we can find arc BC and arc AB, and so we can find angle ACD

Answer 8

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.

Answer 9

in general, use the the idea that inscribed angles that subtend the same arc are equal