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Byju's Answer
Standard X
Mathematics
Apollonius's Theorem
In PQR, M i...
Question
In
△
P
Q
R
, M is the midpoint of side QR. If PQ is
11
cm, PR is
17
cm and QR =
12
cm, find PM.
A
15
cm
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B
13
cm
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C
17
cm
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D
23
cm
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Solution
The correct option is
B
13
cm
In
△
P
Q
R
,
M is the midpoint of side QR ........ given
∴
PM is the median of the triangle.
By Apollonius theorem,
P
Q
2
+
P
R
2
=
2
P
M
2
+
2
Q
M
2
11
2
+
17
2
=
2
P
M
2
+
2
(
1
2
Q
R
)
2
121
+
289
=
2
P
M
2
+
2
(
6
)
2
410
=
2
P
M
2
+
72
2
P
M
2
=
338
P
M
2
=
169
∴
P
M
=
13
cm ........Taking sq. roots
So, option B is correct.
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Similar questions
Q.
In triangle PQR, PQ = 8 cm, PR = 17 cm and QR = 15 cm. The angle Q (in degrees) is:
Q.
In ΔPQR, Q is a right angle, the lengths of PQ and PR are 8 cm and 17 cm, respectively. Find the length of QR.
Q.
In
△
PQR, M and N are points on sides PQ and PR respectively such that PM = 15 cm and NR = 8 cm. If PQ = 25 cm and PR = 20 cm state whether MN
∥
QR.
Q.
In ∆PQR, M and N are points on sides PQ and PR respectively such that PM = 15 cm and NR = 8 cm. If PQ = 25 cm and PR = 20 cm state whether MN || QR.