Fill In the Blanks
Short Answer TypeA tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
(a) 12 cm (b) 13 cm
(c) 8.5 cm (d) 
From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is
(A) 7 cm (B) 12 cm
(C) 15 cm (D) 24.5 cm.
In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to
(A) 60° (B) 70°
(C) 80° (D) 90°
Fig. 10.11
Long Answer TypeIf tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠ POA is equal to
(A) 50° (B) 60°
(C) 70° (D) 80°.
Short Answer TypeProve that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
Let AMB and CND be two parallel tangents to a circle with centre O. Join OM and ON. Draw OP || AB.
Now, AM || PO
⇒ ∠AMO + ∠POM = 180°
[Consecutive interior angles]
⇒ 90 + ∠POM = 180°
⇒ ∠POM = 90°
Similarly, ∠PON = 90°
∴ ∠POM + ∠PON = 90° + 90° =180°
Hence, MON is a straight line passing through O.
Long Answer TypeTwo concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
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