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Consider a circle with centre at C. Let OP, OQ denote respectively the tangents to the circle drawn from a point O outside the circle. Let R be a point on OP and S be a point on OQ such that OR × SQ = OS × RP. Which of the following statement(s) is/are correct? (1) If X is the circle with centre at O and radius OR, and Y is the circle with centre at O and radius OS, then X = Y (2) ∠POC + ∠QCO = 90° Select the correct answer using the code given below.

Consider a circle with centre at C. Let OP, OQ denote respectively the tangents to the circle drawn from a point O outside the circle. Let R be a point on OP and S be a point on OQ such that OR × SQ = OS × RP. Which of the following statement(s) is/are correct? (1) If X is the circle with centre at O and radius OR, and Y is the circle with centre at O and radius OS, then X = Y (2) ∠POC + ∠QCO = 90° Select the correct answer using the code given below. Correct Answer Both 1 and 2

⇒ RP = SQ

⇒ OP – RP = OS – SQ

⇒ OR = OS

Statement I:

Both X and Y are circles with same centre and radius

⇒ X = Y

⇒ Statement I is true

In quadrilateral OPCQ

⇒ ∠O + ∠P + ∠Q + ∠C = 360°

⇒ 2∠POC + 90° + 90° + 2∠QCO = 360

⇒ 2∠POC + 2∠QCO = 180°

⇒ ∠POC + ∠QCO = 90°

⇒ Statement II is true

∴ Both I and II are true.

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