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Selina Solutions Class 9 Mathematics Solutions for Exercise 17(A) in Chapter 17 - Chapter 17- Circles

Question 1 Exercise 17(A)

A chord of length 8 cm is drawn at a distance of 3 cm from the center of a circle. Calculate the radius of a circle.

Answer:

Let AB be the chord and O be the center of the circle.

Let OC be the perpendicular drawn from O to AB.

Selina Solutions CONCISE Maths - Class 9 ICSE chapter Chapter 17- Circles Question 1 Solution image

We know, that the perpendicular to a chord, from the center of a circle, bisects the chord.

Selina Solutions CONCISE Maths - Class 9 ICSE chapter Chapter 17- Circles Question 1 Solution image

Selina Solutions CONCISE Maths - Class 9 ICSE chapter Chapter 17- Circles Question 1 Solution image

Hence, radius of the circle is 5 cm.

Video transcript
"hello students welcome to lido q a video session i am sev your math tutor and question for today is the chord of length 8 centimeter is drawn at a distance of 3 centimeter from the center of the circle calculate the radius of the circle so here radius of the circle is ao we need to calculate ao to calculate ao first of all we have been given that chord a b and center o is present in the figure now oc is the perpendicular drawn from o to a b you can see that and this perpendicular has a characteristic of bisecting a b into ac and c b such that ac will be equal to bc so here you have let a b be the chord and o be the center now let oc be the perpendicular drawn from o to a b now we know that this perpendicular oc will bisect a b as in this case you can see ac is equal to cb that will be the bisection of a b into two equal parts and the call length you have been given that is a b is equal to 8 centimeter and hence ac will be equal to 4 centimeter so here applying the pythagoras property in the right triangle aoc you have ac square plus oc square is equal to ao square so your ac square here will be 4 square plus oc square will be 3 square and ao square is what you have to find the radius so ao square will be equal to 16 plus 9 and that will be 25 so ao square is 25 so your ao will be equal to 5 centimeter so your radius for the circle which is given is 5 centimeters so this is our answer if you have any query you can drop it down in your comments section and subscribe to lido for more such q a thank you for watching"
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