Question : Tangent drawn from a point Y touches the circle at X, O is the centre of this circle. If OY = 50 cm and XY = 40 cm, then what will be the radius of this circle?
Option 1: 60 cm
Option 2: 75 cm
Option 3: 45 cm
Option 4: 30 cm
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Correct Answer: 30 cm
Solution :
Given:
OY = 50 cm and XY = 40 cm
Use the Pythagorean theorem to find the length of OX, which is the radius of the circle [in $\triangle OXY$]
OY
2
= OX
2
+ XY
2
⇒ OX
2
= OY
2
– XY
2
⇒ OX
2
= (50)
2
– (40)
2
⇒ OX
2
= 2500 – 1600 = 900
⇒ OX = $\sqrt{900}$ = 30 cm
Hence, the correct answer is 30 cm.
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