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Constructions

Question
CBSEENMA10008461
Wired Faculty App

A 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)  square root of 119 space cm

Solution
open parentheses straight d close parentheses space space space square root of 119 space cm.

Reason : Radius and tangent are perpendicular to each other.
Thus ∠OPQ is a right angle.
OQ squared equals OP squared plus PQ squared rightwards double arrow space space PQ squared space space equals space OQ squared minus OP squared space space space space space space space space space space space space space equals space 12 squared minus 5 squared space space space space space space space space space space space space space space 144 minus 25 space equals space 119 rightwards double arrow space space space space PQ space equals space square root of 119 space end root space cm.

Some More Questions From Constructions Chapter

A tangent to a circle intersects it in ___________ point(s).

A line intersecting a circle in two points is called a ____________.

A circle many have ______ parallel tangents.

The common point of a tangent and the circle is called ____________.

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

If 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°.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

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