A point P is 25 cm from the centre 'O' of the circle and length of the tangent drawn from 'P' to the circle is 24 cm. Find theradius of the circle.
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Answer- The above question is from the chapter 'Circles'.
Circle- It is a collection of infinite points.
Tangent- It is a line intersecting circle at one point on the circumference.
Radius and tangent are perpendicular to each other at point of contact.
Given question: A point P is 25 cm from the centre 'O' of the circle and length of the tangent drawn from 'P' to the circle is 24 cm. Find the radius of the circle.
Solution: (The diagram has been attached.)
Given- A circle with centre O, length of tangent to circle at point P i.e PQ = 24 cm, OP = 24 cm
To find- Radius of circle (r) i.e. OQ
Sol.- We know that tangent is perpendicular to radius at point of contact.
⇒ OQ ⊥ PQ
⇒ OQP is a right angled Δ.
By Pythagoras Theorem, OQ² + PQ² = OP²
r² + 24² = 25²
r² = 625 - 576
r² = 49
r = ± √49
r = ± 7
r = 7 (∵ radius can't be negative.)
r = 7 cm
∴ Radius of the circle (r) i.e. OQ = 7 cm.
