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## Question 25. In the adjoining figure, ABCD is a cyclic quadrilateral.The line PQ is the tangent to the circle at A. If ∠CAQ : ∠CAP = 1 : 2, AB bisects ∠CAQ and AD bisects ∠CAP, then find the measure of the angles of the cyclic quadrilateral. Also prove that BD is a diameter of the circle.

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This is the basic and conceptual question from Chapter name- circles Topic – Angle properties of circles Chapter number- 15 In ...Read more

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## Question 22. (a) In the figure (i) given below, O is the centre of the circle and SP is a tangent. If ∠SRT = 65°, find the value of x, y and z. (2015) (b) In the figure (ii) given below, O is the centre of the circle. PS and PT are tangents and ∠SPT = 84°. Calculate the sizes of the angles TOS and TQS.

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This is circle based question from Chapter name- circles Topic – Angle properties of circles Chapter number- 15 In this question ...Read more

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## Question 21. (a) In the figure (i) given below, PQ is a tangent to the circle at A, DB is a diameter, ∠ADB = 30° and ∠CBD = 60°, calculate (i) ∠QAB (ii) ∠PAD (iii) ∠CDB.

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This is circle based question from Chapter name- circles Topic – Angle properties of circles Chapter number- 15 In the figure ...Read more

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## Question 20. In the given figure, tangents PQ and PR are drawn from an external point P to a circle such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ, Find ∠RQS

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This is the basic and conceptual question from Chapter name- circles Topic – Angle properties of circles Chapter number- 15 In ...Read more

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## Question 19. In the given figure, AD is a diameter of a circle with centre O and AB is tangent at A. C is a point on the circle such that DC produced intersects the tangent of B. If ∠ABC = 50°, find ∠AOC.

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One of the most important and exam oriented question from Chapter name- circles Topic – Angle properties of circles Chapter ...Read more

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## Question 18. (a) In the figure (i) given below, PA and PB are tangents at a points A and B respectively of a circle with centre O. Q and R are points on the circle. If ∠APB = 70°, find (i) ∠AOB (ii) ∠AQB (iii) ∠ARB (b) In the figure (ii) given below, two circles touch internally at P from an external point Q on the common tangent at P, two tangents QA and QB are drawn to the two circles. Prove that QA = QB.

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This is circle based question from Chapter name- circles Topic – Angle properties of circles Chapter number- 15 In first part ...Read more

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## Question 17. Two circles with centres A, B are of radii 6 cm and 3 cm respectively. If AB = 15 cm, find the length of a transverse common tangent to these circles.

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One of the most important and exam oriented question from Chapter name- circles Topic – Angle properties of circles Chapter ...Read more

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## Question 16. In the given figure, AC is a transverse common tangent to two circles with centres P and Q and of radii 6 cm and 3 cm respectively. Given that AB = 8 cm, calculate PQ.

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This is the basic and conceptual question from Chapter name- circles Topic – Angle properties of circles Chapter number- 15 In ...Read more

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## Question 15. Calculate the length of a direct common tangent to two circles of radii 3 cm and 8 cm with their centres 13 cm apart.

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One of the most important and exam oriented question from Chapter name- circles Topic – Angle properties of circles Chapter ...Read more

• 1

## Question 14. The length of the direct common tangent to two circles of radii 12 cm and 4 cm is 15 cm. Calculate the distance between their centres

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This is the basic and conceptual question from Chapter name- circles Topic – Angle properties of circles Chapter number- 15 We ...Read more