00:01
So we have ob and oc that are two straight lines and then d is a point on bc.
00:10
So here is d and the distance from b to d, the ratio from b to d to compare to d to d that is equivalent to m over n.
00:28
So this distance here is in the ratio m to n.
00:37
Okay, well, let's just call these distances m and n then.
00:41
Then i get that n times bd is equal to m times d c in terms of length.
01:03
And what else do we want to know? okay, so we want to know that proof that o -d, is equal to n times ob, plus m times oc divided by n plus m.
01:23
Okay.
01:26
Well, here is od.
01:44
So let's see here.
01:46
Here is, oh, this is not a, this is o.
01:54
Okay, so we have ob, we have oc, and i want, od.
02:01
Well, if i look at this triangle here, b .c.
02:14
Is equal to bd plus d .c.
02:23
And those are in the same direction.
02:25
So the measure then of bc is the measure of bd plus dc, which is m, also let's see here, bc, which is this here, is this here, is equal to ob minus oc.
03:27
And let me rephrase that.
03:29
So let's see here.
03:32
O .c is equal to ob plus b .c.
03:40
So that means then that bc is equal to ob, no, oc minus ob...