In a non-right-angled triangle △PQR, let p, q, r denote the lengths of the sides opposite to the angles at P,
Q, R respectively. The median from R meets the side PQ at S, the perpendicular from P meets the side QR
at E, and RS and PE intersect at O. If p = √3 , q = 1, and the radius of the circumcircle of the △PQR equals
1, then which of the following options is/are correct?
A. length of OE = 1
6
B. Radius of incircle of △PQR = √3 (2-√3)
2
C. Length of RS = √7
2
D. Are of △SOE = √3
12
Answers
Answered by
0
Answer:
1. length of OE = 16
2. area of SOE = √312
Hope this would help.....
Answered by
1
Step-by-step explanation:
sinP
p
=
sinQ
q
=2(1)⇒sinP=
2
3
,sinQ=
2
1
⇒∠P=60
∘
or 120
∘
and ∠Q=30
∘
or 150
∘
because ∠P+∠Q must be less than 180
∘
but not equal to 90
∘
∠P=120
∘
and ∠Q=30
∘
and ∠R=30
∘
sinR
r
=2⇒r=1
Now length of median RS=
2
1
2p
2
+2q
2
−r
2
=
2
1
6+2−1
=
2
7
⇒ option (A) is correct
Inradius =
p+q+r
2△
=
p+q+r
4×(1)
2pqr
=
2
1
(
1+1+
3
1×1×
3
)=
2
3
(
1
2−
3
)⇒ option (C) is correct
⇒
2
1
×
3
×PE=
4(1)
pqr
(equal area of △)⇒PE=
4
1×1×
3
×
3
2
=
2
1
⇒OE=
QR
2(Area of△OQR)
=
3
2×
3
1
(
2
1
.1.
3
sin30
∘
)
=
6
1
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