Question

A point P is 25cm away from the centre of a circle and the length of tangent drawn from P to the circle is 24cm.find the radius of the circle​

Answer 1

Given that,

• A point P is 25 cm away from the centre of a circle. Centre of the circle is O. And, the length drawn from point P to the circle is 24 cm. TP is 24 cm.

⠀⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{Using\;Circle\; Theorem\: :}}$⠀⠀⠀⠀

⠀⠀⠀⠀

• Tangent drawn from an external point (P) is perpendicular to the radius at the point of Contact, O.

Therefore, OT $\perp$ PT.

$\rule{250px}{.3ex}$

⠀⠀⠀

$\underline{\pink{\bigstar\:\sf{By\: Using\; Pythagoras\: Theorem\;In\;\triangle\;OTP\; :}}}$⠀⠀

⠀⠀⠀⠀

$:\implies\sf (OP)^2 = (OT)^2 + (PT)^2 \\\\\\:\implies\sf (OT)^2 = (OP)^2 - (PT)^2 \\\\\\:\implies\sf (OT)^2 = (25)^2 - (24)^2 \\\\\\:\implies\sf (OT)^2 = 625 - 576 \\\\\\:\implies\sf (OT)^2 = 49 \\\\\\:\implies\sf OT = \sqrt{49} \\\\\\:\implies\underline{\boxed{\frak{\pink{OT = 7\;cm}}}}\;\bigstar$

⠀⠀⠀⠀

$\therefore{\underline{\textsf{Hence, \; required\; radius\;of\;the\;circle\;is\;\textbf{7 cm}.}}}$⠀

Answer 2

Answer:

Given :-

• Point p = 25 cm
• Tangent length = 24 cm

To Find :-

Radius of circle

Solution :-

By using Pythagoras theorem

B² = H² - P²

B² = (25)² - (24)²

B² = 625 - 576

B² = 49

B = √49

B = 7.

Radius of circle is 7 cn