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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


Team Careers360 25th Jan, 2024
Answer (1)
Team Careers360 27th Jan, 2024

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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