If the Tangent at Point P to the Circle with Center O Cuts a Line Through O at Q Such that Pq = 24cm and Oq = 25 Cm. Find the Radius of Circle - Mathematics

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

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Solution

Given,

PQ = 24 cm

OQ = 25 cm

OP = radius = ?

P is point of contact, At point of contact, tangent and radius are perpendicular to each other

∴ ΔPOQ is right angled triangle ∠OPQ = 90°

By Pythagoras theorem,

𝑃𝑄2 + 𝑂𝑃2 = 𝑂𝑄2

⇒ 242 + 𝑂𝑃2 = 252

⇒`PO = sqrt((25)^2 − (24)^2) = sqrt(625 − 576)`

= `sqrt(49)` = 7𝑐𝑚

∴ 𝑂𝑃 = 𝑟𝑎𝑑𝑖𝑢𝑠 = 7𝑐𝑚

 

 

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Chapter 8: Circles - Exercise 8.1 [Page 5]

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RD Sharma Class 10 Maths
Chapter 8 Circles
Exercise 8.1 | Q 4 | Page 5

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