Q2 of 47 Page 10

Find the length of the tangent from a point which is at a distance of 5 cm from the centre of the circle of radius 3 cm.


Given: PQ is a tangent to the circle intersect at Q. OP = 5 cm and OQ = 3 cm.
To find: PQ
Proof:
In rt.Δ OQP, by Pythagoras theorem
PQ = ==== 4 cm
Therefore the length of the tangent from a point is 4 cm.

More from this chapter

All 47 →
1 Prove that the line segment joining the points of contact of two parallel tangents to a circle is a diameter of the circle. 3 Find the locus of centres of circles which touch a given line at a given point. 4 In two concentric circles, prove that all chords of the outer circle which touch the inner circle are of equal length. 5 Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.