The common chord of the two circles, c1 and c2, is 3.8 cm long. This chord forms an angle of 47° with the radius r1 in the circle c1. An angle of 24° 30' with the radius r2 is formed in the circle c2. Calculate both radii and the distance between the two centers of the circles.  Did you find an error or inaccuracy? Feel free to write us. Thank you! Thank you for submitting an example text correction or rephasing. We will review the example in a short time and work on the publish it. We encourage you to watch this tutorial video on this math problem: video1
Question 5 Circles Exercise 12A Next
Answer:
Consider AB and CD as the chords of a circle with centre O It is given that AB = 30cm and CD = 16cm Join the lines OA and OC We know that AO = 17cm and CO = 17cm Construct OM ⊥ CD and OL ⊥ AB The perpendicular from the centre of a circle to a chord bisects the chord We know that AL = ½ × AB By substituting the values AL = ½ × 30 So we get AL = 15cm We know that CM = ½ × CD By substituting the values CM = ½ × 16 So we get CM = 8cm Consider △ ALO Using the Pythagoras theorem it can be written as AO^2 = OL^2 + AL^2 By substituting the values 17^2 = OL^2 + 15^2 So we get OL^2 = 17^2 - 15^2 On further calculation OL^2 = 289 – 225 By subtraction OL^2 = 64 By taking the square root OL = √64 OL = 8cm Consider △ CMO Using the Pythagoras theorem it can be written as CO^2 = CM^2 + OM^2 By substituting the values 17^2 = 82 + OM^2 So we get OM^2 = 17^2 - 8^2 On further calculation OM^2 = 289 – 64 By subtraction OM^2 = 225 By taking the square root OM = √225 OM = 15cm So the distance between the chords = OM + OL By substituting the values Distance between the chords = 8 + 15 = 23cm Therefore, the distance between the chords is 23 cm.
Video transcript "hi students welcome to leader learning so here i am your leader tutor archer who will help you to simplify this question the question we have is two parallel chords of length 30 centimeter 16 centimeter are drawn on the opposite side of center of the circle of radius 17 centimeter find the distance between the coils so some figure will look like a circle we can draw a figure first it's a question of a circle so first step is to always draw a circle so two parallel chords let's consider the two parallel chords the chord has one of the chord and the second chord and a center of course so now the two chords let's consider the second chord as a b the first chord as cd now drawn on the opposite side of center yes the circle of the radius 17 let's draw the circ radius as 17. let's join this radius then we are drawing two radius this is 17 this is total 30 a b one of the chords second chord is 16. what we needs to find we need to find out the distance between the chords so this is the distance between the quads from the center to the another center like this let's name the center as o the points they are joining so we need to find out the center this distance so the figure will somewhat look like this now using this figure the a o and c o it's already 17 a b is given to us 13 and c d we have considered 16. so let's write all these things here so a b and c d are the two chords are the two chords everything we need to write out because nothing is given in the question and we have to write that what is called what is radius so a b is given that is 30 that and cd is 16. now om is the perpendicular from perpendicular to a cd so it's the perpendicular so it makes the angle 90 that means it bisects bisect cd that means cm will be equals to md which will be equals to half of 60 that is 8 so this part now will be 8 and 8 this is 8 this is also 8 the second part now o l is perpendicular to a b that means and again it bisects a b so a l will be equals to l b that is again equals to half of a b half of 30 that is 15 so this is what again we know so let's replace this terms it is 15 and it's also 50 and we need to calculate that is ml ml is equals to what so how we will do it is what we will do for ml is we will find out ml is equal to we can say m o plus l o l if we can find out this m o and o l we will add them and we'll get m l so this is what we will do now look at both these triangles both this triangle c m o and o a l both are right angle so we'll apply that and then find out the value so triangle here we'll apply the triangle triangle like this this is m this is c and this is 90 is 8 and 17 and this is what we need to find out so here in the triangle c m o c o square is b equals to c m square plus m o square c m is eight square plus m o will remain as it is and it's 17 square so it's 289 is equals to 64 plus m o square now subtract the terms together so 289 minus 64 will give us the answer 289 minus 64 will give us the answer as 225 is equals to mo square so mo will be equals to under root 225 that will be equals to 15 so m o is 15 so this is 15 now second we will similarly will do the second part so second triangle that is the triangle a o l here is a triangle it's the o at the center and it's l so o a and and again it's a 90 it's 17 it's 15 and o l will calculate so in that triangle a o l a o square is equals to o l square plus a l square a o square is 17 square is equals to a l is 15 square plus o l square as it is now 15 square is 225 plus o l square is equals to 289 289 minus 225 is equals to o l square so o l will square will be equals to 64 o l is equals to 64 under root and thus o l is equals to eight now we know the o l so we can find out the from here we can find out the the equation so ol is 8 this is 8 and this is 15 so we'll add them 15 plus 8 and l is equals to mo plus ol this 8 plus 15 that is equals to 23 so ml is equals to 23 centimeter all these are in the centimeters form so you must write the centimeter so it's 23 centimeter and this is our final answer that is m l is equals to 23 i hope you understood this question this will be simplified if you have the doubt please write in the comment section for regular updates subscribe to the leader channel thank you "
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What is the distance from the center of a circle of radius 17cm to a chord whose length is 30 cm?
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