Q12 of 31 Page 218

In the adjoining figure O is the centre and BOA is a diameter of the circle. A tangent drawn to a circle at the point P intersects the extended BA at the point T. If ∠PBO = 30°, let us find the value of ∠PTA.

∠ PBO = 300 (Given)


∠ OPB = 300 (Δ PBO is an isosceles triangle)


∠ OPT = 900 (Tangents are perpendicular to the line joining the centre of the circle)


∠ BPT = (900 + 300) = 1200


∠ PTA = 1800–(1200 + 300) = 300 (Sum of interior angles of Δ BPT)


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11

Let us write whether the following statements are true of false:

(i) P is a point inside a circle. Any tangent drawn on the circle does not pass through the point P.


(ii) There are more than two tangents can be drawn to a circle parallel to a fixed line.

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Let us fill in the blanks.

(i) If a straight line intersects the circles at two points, then the straight line is called ______of circle.


(ii) If two circles do not intersect or touch each other, then the maximum number of common tangents can be drawn is ________.


(iii) Two circles touch each other externally at the point A. A common tangent drawn to two circles at the point A is _______ common tangent (direct/transverse)

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In the adjoining figure, ΔABC circumscribed a circle and touches the points P,Q,R. If AP = 4 cm, BP = 6cm, AC = 12 cm and BC = x cm, let us determine the value of x.

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In the adjoining figure, three circles with centre A, B, C touch one another externally. If AB = 5 cm, BC = 7 cm and CA = 6 cm, let us find the length of radius of circle with centre A.