Question

In figure, line l touches the circle with centre o at point p. Q is the midpoint of radius op. RS is the chord through Q such that chords RS parallel to line l. If RS =12. Find radius

Answer 1

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Let's say radius of the circle is r.

In the given figure,

OP= OR = Radius = r

Since, OP is perpendicular to l and l || RS.

Hence,

Radius OP is perpendicular to RS (chord)

RQ = QS = 6 units

As Q is midpoint of OP

So, OQ = r/2

Using Pythagoras theorem, in ∆OQP,

OR^2 = OQ^2 + RQ^2

r^2 =(r/2) ^2+ 6^2

4r^2 = r^2 + 144

3r^2 = 144

r^2 = 48 or r = 7 units

Hence, The radius of the circle is approx 7 unit.

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