Question

ii) PR is a chord of a circle with centre 0. IfQ
is a point on the chord PR such that PQ
QR. Then the measure of angle OQR is​

Answer 1

Answer:

We know, that radius is perpendicular to a tangent .

∴ ∠OPR=90

⇒ ∠OPQ+∠QPR=90

⇒ ∠OPQ+50

=90

⇒ ∠OPQ=90

−50

⇒ ∠OPQ=40

⇒ OP=OQ [ Radii of a circle ]

⇒ ∠OPQ=∠OQP=40

[ Base angles of equal sides are also equal ]

In △POQ,

⇒ ∠OQP+∠POQ+∠OPQ=180

⇒ 40

+∠POQ+40

=180

⇒ ∠POQ+80=180

⇒ ∠POQ=100

Hope it helps!