# Long Answer Type Questions: Circles - Mathematics (Maths) Class 9

Question 1. Look at the adjoining figure. If O is the centre of the circle and ST = 3 cm, then find the radius of the circle when RS ⊥ PQ.
Solution
: Let us join O and P such that OP = r.
∵ RS ⊥ PQ
∴ T is the mid-point of PQ.

⇒ PT = (1/2) PQ
⇒ PT = (1/2) x 12 cm = 6 cm                 [∵ PQ = 12 cm      (Given)]
And ∠ OTP = 90°
Also OS = r and TS = 3 cm
∴ OT = OS - TS = (r - 3) cm
Now, in right ΔOTP, we have, OP2 = PT2 + OT2
⇒ r= 62 + (r - 3)2
⇒ r2 = 36 + r+ 9 -  6r
⇒ 6r = 45

⇒ r =(45/6) = (15/2) = 7.5 cm
Thus, the radius of the circle is 7.5 cm.

Question 2. An equilateral triangle is inscribed in a circle. Find the radius of the circle.
Solution:
Let ABC be an equilateral triangle such that AB = BC = AC = 9 cm                  (each)
Let us draw a median AD corresponding to BC.
∴ BD =(1/2) BC
⇒ BD = (1/2) x 9 cm = (9/2)cm
Also, AD ⊥ BC                  [∵ O is the centre of the circle]

Since, in an equilateral triangle, the centroid and circumcentre coincide.

∴ AO: OD = 2:1

⇒

Thus, the required radius =  3√3 cm

The document Long Answer Type Questions: Circles | Mathematics (Maths) Class 9 is a part of the Class 9 Course Mathematics (Maths) Class 9.
All you need of Class 9 at this link: Class 9

## FAQs on Long Answer Type Questions: Circles - Mathematics (Maths) Class 9

 1. What is a circle?
Ans. A circle is a closed curved shape in which all points on the curve are equidistant from a fixed point called the center.
 2. What is the formula to find the circumference of a circle?
Ans. The formula to find the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius of the circle.
 3. How is the area of a circle calculated?
Ans. The area of a circle is calculated using the formula A = πr^2, where A represents the area and r represents the radius of the circle.
 4. What is the relationship between the diameter and the radius of a circle?
Ans. The diameter of a circle is twice the length of its radius. In other words, if r represents the radius, then the diameter (d) can be expressed as d = 2r.
 5. How do you find the radius of a circle if you only know the circumference?
Ans. To find the radius of a circle if you only know the circumference (C), you can use the formula r = C/(2π), where r represents the radius.

## Mathematics (Maths) Class 9

62 videos|426 docs|102 tests

## Mathematics (Maths) Class 9

62 videos|426 docs|102 tests

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