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## Ques (b) In the figure (ii) given below, O and O’ are centres of two circles touching each other externally at the point P. The common tangent at P meets a direct common tangent AB at M. Prove that: (i) M bisects AB (ii) ∠APB = 90°.

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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 39. (a) In the figure (i) given below, AB is a chord of the circle with centre O, BT is tangent to the circle. If ∠OAB = 32°, find the values of x and y

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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 38(b) In the figure (ii) given below, two circles with centres C, C’ intersect at A, B and the point C lies on the circle with centre C’. PQ is a tangent to the circle with centre C’ at A. Prove that AC bisects ∠PAB.

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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 38. (a) In the figure (i) given below, two circles intersect at A, B. From a point P on one of these circles, two line segments PAC and PBD are drawn, intersecting the other circle at C and D respectively. Prove that CD is parallel to the tangent at P.

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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 37. If the sides of a rectangle touch a circle, prove that the rectangle is a square.

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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 36. In the adjoining figure ∆ABC is isosceles with AB = AC. Prove that the tangent at A to the circumcircle of ∆ABC is parallel to BC.

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

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## Ques 35(b) In the figure (ii) given below, A, B and C are three points on a circle. The tangent at C meets BA produced at T. Given that ∠ATC = 36° and ∠ACT = 48°, calculate the angle subtended by AB at the centre of the circle.

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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 35. (a) In the figure (i) given below, AT is tangent to a circle at A. If ∠BAT = 45° and ∠BAC = 65°, find ∠ABC.

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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 34. Two chords AB, CD of a circle intersect externally at a point P. If PA = PC, Prove that AB = CD.

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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 33. (a) In the figure (i) given below, PAB is secant and PT is tangent to a circle. If PA : AB = 1:3 and PT = 6 cm, find the length of PB. (b) In the figure (ii) given below, ABC is an isosceles triangle in which AB = AC and Q is mid-point of AC. If APB is a secant, and AC is tangent to the circle at Q, prove that AB = 4 AP

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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