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## O is the centre of a circle of radius 8 cm. The tangent at a point A on the circle cuts a line through O at B such that AB = 15 cm. Find OB.

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we have to find that line from that tangent AB

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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 31. PAB is secant and PT is tangent to a circle (i) PT = 8 cm and PA = 5 cm, find the length of AB. (ii) PA = 4.5 cm and AB = 13.5 cm, find the length of PT.

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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 30(b) In the figure given below, diameter AB and chord CD of a circle meet at P. PT is a tangent to the circle at T. CD = 7.8 cm, PD = 5 cm, PB = 4 cm. Find (i) AB. (ii)the length of tangent PT.

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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 30. (a) In the figure (i) given below, PT is a tangent to the circle. Find TP if AT = 16 cm and AB = 12 cm.

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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 29. Two chords AB, CD of a circle intersect internally at a point P. If (i) AP = cm, PB = 4 cm and PD = 3 cm, find PC. (ii) AB = 12 cm, AP = 2 cm, PC = 5 cm, find PD. (iii) AP = 5 cm, PB = 6 cm and CD = 13 cm, find CP.

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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 28(b) In the figure (ii) given below, O is the centre of the circle and PT is the tangent to the circle at P. Given ∠QPT = 30°, calculate (i) ∠PRQ (ii) ∠POQ.

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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 28. (a) In the figure (i) given below, O is the centre of the circumcircle of triangle XYZ. Tangents at X and Y intersect at T. Given ∠XTY = 80° and ∠XOZ = 140°, calculate the value of ∠ZXY.

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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 27(b) In the figure (ii) given below, AP and BP are tangents to the circle with centre O. Given ∠APB = 60°, calculate. (i) ∠AOB (ii) ∠OAB (iii) ∠ACB.

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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 26. In a triangle ABC, the incircle (centre O) touches BC, CA and AB at P, Q and R respectively. Calculate (i) ∠QOR (ii) ∠QPR given that ∠A = 60°.

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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