Q. 33.7( 19 Votes )

# If the tangent at a point P to a circle with centre O cuts a line through O at Q such that PQ = 24 cm and OQ = 25 cm. Find the radius of the circle.

Answer :

**Given:** PQ = 24 cm

OQ = 25 cm

**To find:** The value of OT.

**Theorem Used:**

1.) A tangent to a circle is perpendicular to the radius through the point of contact.

2.) Pythagoras theorem:

In a right-angled triangle, the squares of the hypotenuse is equal to the sum of the squares of the other two sides.

**Explanation:**

Since QT is a tangent to the circle at T and OT is radius,

Therefore, by the theorem stated, OT perpendicular QT

In ΔOTQ,

By Pythagoras theorem we have

OQ^{2} = OT^{2} + TQ^{2}

For the given values,

⇒ OT^{2} = 25^{2} – 24^{2}

⇒ OT^{2} = 625 – 576

⇒ OT^{2} = 49

⇒ OT = √49

⇒ OT=7 cm

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