ABD=ACD(angles subtended from the same chord)
:. FBD=FCA (angles on a straight line are supplementary)
But FBD+FCA=180 (opposite angles of a cyclic quad are supplementary)
:. FDB=180/2=90
I got those answers but didnt gave a really retarded proof coz i knew by looking at it it was a right angle.
Then i just wrote that the line was = 2r. pure guess. I hope i get marks.
yea i fudged that question aswell.. shouldve read the whole thing.. coz i assumed the cyclic quad was the one in the diagram, (the one with a circle around it!)
i said let sum angle = a, let the other one = b, so whatevvr angle = a +b
any chance at one out of the 2 marks?!
second part AD = rM, where M is a variable ? doubt that'd get the one mark
lol dude i did everything in algebra.
i didnt know you could assume that AD was diameter. for ii i go
Construct DX such that DX is a diameter of the circle
then i go DX = (2r)<sup>2</sup> = pythagoras bla.
you can say that AD is the diameter when you prove either < ABD or < ACD to be 90º. Then you can say it is diameter because AD subtends the right angle at the circumference.
It's a 1 marker, for the length of the line to be a simple function of r, the angle must be 90 degrees. Man, answer by inspection is so so much easier than actually doing anything.
Damn diagram, so misleading. They drew angles so wrong. How can two opposite angles of a cyclic quad add to equal 180 when they're drawn to be both obtuse... *grumble grumble * "not to scale" *grumble grumble*