 Hello friends, so we have taken a problem here to solve with the theorems. We learned in the previous videos So let us solve this problem. The question says the radius of a circle is 13 centimeter and One of its chord is 10 centimeter. We have to find the distance of the chord from the center. So as you can see Oh is the center here. Oh, oh, it happens to be 13 centimeter AB is the chord with length 10 centimeter. Okay, so This is how systematically you should solve the problem given is radius of Circle with Center oh Is equal to 13 centimeter AB is a chord of the circle and AB is equal to 10 centimeter Okay to find To find Distance Distance of chord AB From oh Okay, so what do we need to do we need to actually construct something here construction is required So what is distance anyways if you want to measure distance from a point for a particular line What is that? It's nothing but the length of the perpendicular dropped from the point on to the line, right? So hence construction is OC perpendicular to AB drawn Okay, OC perpendicular to AB is drawn. So this is 90 degrees Okay, OC a is 90 degree. Hmm. So now solution how to find value of OC so AC is equal to half AB is equal to five centimeter Why because perpendicular from Center on a chord on A chord bisects the chord bisects Bisects the chord isn't it we studied this in previous sessions if you have not learned this theorem I would suggest go back into the previous sessions and see where this theorem has been discussed So if you drop any perpendicular, so let's say there is a perpendicular here and you drop The perpendicular to this then we know that this bisects the chord how you know that this was the proof So this side is equal to this side. This is common and 90 degree in each. So by RHS congruency these two triangles will be congruent So hence this side will be equal to this side. Correct. So by the same logic here AC is equal to five. So I can write this is five five centimeter five centimeter right now in triangle OAC OAC I have to just find OC now, right? So, you know by Pythagoras theorem OA square is equal to OC square plus AC square right by Pythagoras Pythagoras's Theorem we have been learning this term since childhood. So now you can find out OC Very clearly OC square is OA square minus AC square Right OA square is 13. So 13 square minus AC is 5 square So hence you'll get 169 minus 25 Which is 1 4 4 right therefore? OC is equal to under root 1 4 4 Is equal to 12 and the units were centimeter. So hence we could find out OC, right? This is the solution. Okay, so hence what is the learning? So learning is the application of the theorem perpendicular from center of a chord Center on a chord bisect the chord and then Pythagoras theorem. So these are the two things which we applied in this particular Problem okay, and hence we got the result as 12 centimeter. Okay