1.

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»

>

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}.}}}⠀


Discussion

No Comment Found

Related InterviewSolutions