Hình 9A1 Bài 2 #toan9

ABC triangle is inscribed in a circle with center O and the diameters AD BE and CF are complete The diameters AD BE CF Call M N P the midpoints of BC M is the midpoint of BC N is the midpoint of CA and P is the midpoint of AB Prove that DM NE PF are concurrent Now let's think a bit about the surface so that we can understand the problem better Does the problem involve right angles because the diameter creates a right angle Each point on the circle views the diameter at a right angle Each diameter combined with two vertices leaves two right angles so we will have quite a few right angles If I draw everything out the image would look messy and unattractive That's right it would look complicated isn't it So this kind of situation They usually only observe one diameter to find the general rule Since it is related to the right angle with the sides we can draw the orthocenter H Because it is related to a right angle for example here we have this angle which is a right angle So we draw the orthocenter H by this perpendicular line and this perpendicular line Then we will get the correct quadrilateral BHCD right We will be given the BHCD training When I draw the orthocenter like this it will form parallel elements If you are familiar with this configuration you will automatically know and have an immediate reaction to the fact that we are drawing the orthocenter H Sometimes when doing geometry I didn't intentionally draw an auxiliary figure but it seemed like an automatic mechanism made me react that way These movements form during our work and practice When people practice a lot they work a lot Unconsciously it may form habits and skills in drawing auxiliary lines or adding new points Without too much effort but it is very automatic it is called a conditioned reflex people will progress without realizing it when they work a lot When drawing the orthocenter it is very fast we will observe the parallelograms For example in the parallelogram BHCD we have BH and CD both perpendicular to AC Therefore BH and CD are parallel to each other Similarly CH is perpendicular it is also perpendicular to AB Since BD is perpendicular to AD because of the diameter we have a right angle at B and we have a parallelogram right away BHCD has two pairs of opposite parallel sides so it is a parallelogram M is the midpoint of BC In a parallelogram the two diagonals intersect at the midpoint of each diagonal the problem states that M is the midpoint of BC meaning that M is collinear with D and H What does this mean This means that our MD which the deck refers to DM is going through absorption Then with such a mindset it is completely similar to the NOE and PF the role of which is to insulate the MD So it will also go through the process So do we have a solution option No need to say much right Now let's go over the main steps of the solution what should we do Let the students try to explain in the class and see if it's okay Step 1 we draw on the line of sight is that correct Step 2 we prove tha BHCD is a parallelogram then I can conclude that MD will pass through the center then the students just need to say that similarly we have NOE and PF also passed through in exactly the same way right That's it From this problem what should we pay attention to Usually after finishing a problem it's an opportunity for me to reflect on my experience to improve myself The way of thinking or the refinement of habits One is to prove the three equal lines and the other is to point out one point All three roads pass through but in today's situation I just need to point out the location of MD Just point out where MD passes through In which the node plays an equal role for the NOE and PF paths we only need to indicate the node Monday is actually the person who set the question they have a model like this then they remove the attraction point they hide a factor Then people tried to restate the problem That's why many things are actually the same in essence but are expressed in different forms externally it's just that if we do many things and accumulate much meaning It is mostly about configuration detecting and explaining is very convenient in fact it is still persistent and diligent work Whoever likes geometry can learn how to come up with exercises like this For example if I create something a little bit it can make me happy and give me more motivation to study