ABCD is a square, having side 12cm, in which ABC and ABD are two quadrant of a circle. If a circle is drawn touching both the quadrants and the square as shown in figure as show in figure given below, then find the area of circle.

Correct Option - 1


Detailed Solution:

Let the radius of circle be ‘r’

In D QPB

OP = 12 – r

PB = 6

QB = 12 + r

(12+r)² = (12–r)² + 6²

r = ¾

Area of circle = pr²

= 22/7 × 3/4 × 3/4

= $\frac{99}{56}sqcm$

<div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1754907255phpHTwNtF.jpeg" alt="" width="197" height="170" loading="lazy"></picture></div><div class="figure"><p><span lang="EN-IN">Let the radius of circle be ‘r’</span></p><p><span lang="EN-IN">In </span><span lang="EN-IN">D</span><span lang="EN-IN"> QPB </span></p><p><span lang="EN-IN">OP = 12 – r</span></p><p><span lang="EN-IN">PB = 6</span></p><p><span lang="EN-IN">QB = 12 + r</span></p><p><span lang="EN-IN"> (12+r)² = (12–r)² + 6²</span></p><p><span lang="EN-IN">r = ¾</span></p><p><span lang="EN-IN">Area of circle = </span><span lang="EN-IN">p</span><span lang="EN-IN">r²</span></p><p><span lang="EN-IN">= 22/7 × 3/4 × 3/4</span></p><p><span lang="EN-IN">= &lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1816433167"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;</span><span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>9</mn> <mn>9</mn> </mrow> <mrow> <mn>5</mn> <mn>6</mn> </mrow> </mfrac> <mi>s</mi> <mi>q</mi> <mtext> </mtext> <mtext> </mtext> <mi>c</mi> <mi>m</mi> </mrow> </math> </span></p></div></div>

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