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In the figure above, points P, Q, R, S, and T lie on a line. Q is the
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13 Dec 2023, 01:15
13 Dec 2023, 01:15
Expert Reply
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Question Stats:
90% (02:15) correct
9% (04:18) wrong based on 11 sessions
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In the figure above, points P, Q, R, S, and T lie on a line. Q is the center of the smaller circle and R is the center of the larger circle. P is the point of contact of the two circles, S is a point on the smaller circle, and T is a point on the larger circle. If RS = 1 and ST = 4, what is the area of the region inside the larger circle but outside the smaller circle?
Show: ::
50.24
Re: In the figure above, points P, Q, R, S, and T lie on a line. Q is the
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13 Jan 2024, 06:25
13 Jan 2024, 06:25
Expert Reply
Post A Detailed Correct Solution For these FRESH Quant & Verbal Questions And Get A Kudos
Re: In the figure above, points P, Q, R, S, and T lie on a line. Q is the
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09 Jun 2024, 12:29
09 Jun 2024, 12:29
Expert Reply
Required area = (Area of bigger circle with center R)– (Area of smaller circle with center Q
\(= \pi \times PR^2 - \pi \times PQ^2\)
We know that:
RS = 1and ST = 4
\(>RT=1+4=5\)
\(>PR=RT=5\)
Also, we have:
\(PS = PT– ST\)
\(= 2 * PR–ST\)
\(= 10– 4=6\)
\(>PQ+QS=6\)
\(>2 * PQ=6\)
\(>PQ=3\)
Thus, we have:
PR = 5 and PQ=3
Thus, required area
\(= \pi \times PR^2 - \pi \times PQ^2\)
\(= \pi (5^2-3^2)\)
\(=16 \pi\)
\(= \approx 50.24\)
\(= \pi \times PR^2 - \pi \times PQ^2\)
We know that:
RS = 1and ST = 4
\(>RT=1+4=5\)
\(>PR=RT=5\)
Also, we have:
\(PS = PT– ST\)
\(= 2 * PR–ST\)
\(= 10– 4=6\)
\(>PQ+QS=6\)
\(>2 * PQ=6\)
\(>PQ=3\)
Thus, we have:
PR = 5 and PQ=3
Thus, required area
\(= \pi \times PR^2 - \pi \times PQ^2\)
\(= \pi (5^2-3^2)\)
\(=16 \pi\)
\(= \approx 50.24\)
