Question

A point p is 25cm from the center O of the circle .then length of the tangent drawn from P to the circle is24cm .find the radius of the circle
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Answer 1

Answer:

Hope it works.............................................™✌️✌️

Answer 2

GIVEN:

• Tangent = XY
• Point of contact = P
• OQ = 25 cm
• The length of the Tangent of a circle = 24 cm i.e., PQ = 24 cm

TO FIND:

• What is the radius of the circle ?

PROCEDURE:

Let the radius of the circle be 'r' cm

【We know that,the Tangent at any point of a circle is perpendicular to the radius through the point of contact.】

Since, XY is a Tangent

∴ OP ⊥ XY

So, OPQ is a right- angled triangle

In ∆OPQ,

➤ ∠ OPQ = 90° [Tangent ⊥ to the radius ]

Using Pythagoras theorem:-

$\sf\red{(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2 }$

According to question:-

$\sf{\mapsto (OQ)^2 = (PQ)^2 + (OP)^2 }$

$\sf{\mapsto (25)^2 = (24)^2 + (OP)^2 }$

$\sf{\mapsto (25)^2 - (24)^2 = (OP)^2 }$

$\sf{\mapsto 625 - 576= OP^2 }$

$\sf{\mapsto 49 = OP^2 }$

$\sf{\mapsto \sqrt{49} = OP }$

$\large\sf\red{\mapsto \: \star \: 7\: cm = OP \: \star }$

❛ Hence, the radius(OP) of the circle is 7cm ❜ 

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✫ Extra Information✫

✬Properties of Tangent ✬ 

➪  The tangent at any point of a circle is perpendicular to the radius through the point of contact. [ Tangent ⊥ Radius ]

➪ The length of Tangents drawn from an external point to a circle are equal.