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Which of the following statements is/are true? A: If two tangents, PA and PB, are formed on a circle from a point ‘P’ and OA and OB are the radius of the circle, then OAPB will be a cyclic quadrilateral. B: In a ΔABC, an incircle is formed with centre ‘O’. Then ∠BAC will be 180° less than the double of the angle made by side BC at the centre of the circle. C: The length of two tangents from a point, outside the circle, are always equal.

Which of the following statements is/are true? A: If two tangents, PA and PB, are formed on a circle from a point ‘P’ and OA and OB are the radius of the circle, then OAPB will be a cyclic quadrilateral. B: In a ΔABC, an incircle is formed with centre ‘O’. Then ∠BAC will be 180° less than the double of the angle made by side BC at the centre of the circle. C: The length of two tangents from a point, outside the circle, are always equal. Correct Answer All A, B and C

GIVEN:

Three statements A, B and C.

CONCEPT:

Properties of circle, chord, tangents, inradius, and circumradius.

FORMULA USED:

No formula.

CALCULATION:

A:

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Since, OA and OB are perpendicular to PA and PB respectively, ∠OAP and ∠OBP will be right angle. So, the sum of ∠AOB and ∠AOB will be 180°. Hence, OAPB will be a cyclic quadrilateral.

B: In a ΔABC, an incircle is formed with centre ‘O’. So, ‘O’ is the incentre of the triangle.

We know that,

∠BOC = 90° + ∠BAC/2

⇒ ∠BAC = 2∠BOC – 180°

C: When two tangents are drawn on a circle from a point, the length of both the tangents is equal.

Hence, statements A, B and C are true.

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