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 midpoint 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, OP^{2} = PT^{2} + OT^{2}
⇒ r^{2 }= 6^{2} + (r  3)^{2}
⇒ r^{2} = 36 + r^{2 }+ 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]
Now, in right ΔADB,
AD^{2} = AB^{2}  BD^{2}
Since, in an equilateral triangle, the centroid and circumcentre coincide.
∴ AO: OD = 2:1
⇒
⇒ Radius = 3√3 cm
Thus, the required radius = 3√3 cm
1. What is a circle? 
2. What is the formula to find the circumference of a circle? 
3. How is the area of a circle calculated? 
4. What is the relationship between the diameter and the radius of a circle? 
5. How do you find the radius of a circle if you only know the circumference? 
62 videos426 docs102 tests

62 videos426 docs102 tests
