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In , the side is produced beyond to a point such that…
MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles
Problem
In
△
P
Q
R
\triangle PQR
△
P
QR
, the side
P
R
PR
P
R
is produced beyond
R
R
R
to a point
S
S
S
such that
∠
Q
R
S
=
∠
Q
P
R
\angle QRS = \angle QPR
∠
QR
S
=
∠
QP
R
. (i) Show that the points
P
,
Q
,
R
P,\,Q,\,R
P
,
Q
,
R
and
S
S
S
are concyclic. (ii) If
∠
Q
P
R
=
35
∘
\angle QPR = 35^\circ
∠
QP
R
=
3
5
∘
and
∠
Q
R
P
=
68
∘
\angle QRP = 68^\circ
∠
QR
P
=
6
8
∘
, find
∠
Q
S
R
\angle QSR
∠
QS
R
giving appropriate reasons.
Related theory
Circles
Cyclic Quadrilaterals
Cyclic quadrilateral properties
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