In Fig. 10.37, PQR = 100°, where P, Q and R are points on a circle with centre O. Find OPR.

Question

In Fig. 10.37, PQR = 100°, where P, Q and R are points on a circle with centre O. Find OPR.

in progress 0
Caroline 2 weeks 2021-09-11T13:25:08+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-11T13:26:24+00:00

    Answer:

    Here, PR is chord

    We mark s on major arc of the circle.

    ∴ PQRS is a cyclic quadrilateral.

    So, ∠PQR+∠PSR=180

    o

    [Sum of opposite angles of a cyclic quadrilateral is 180

    o

    ]

    100+∠PSR=180

    o

    ∠PSR=180

    o

    −100

    o

    ∠PSR=80

    o

    Arc PQR subtends ∠PQR at centre of a circle.

    And ∠PSR on point s.

    So, ∠POR=2∠PSR

    [Angle subtended by arc at the centre is double the angle subtended by it any other point]

    ∠POR=2×80

    o

    =160

    o

    Now,

    In ΔOPR,

    OP=OR[Radii of same circle are equal]

    ∴∠OPR=∠ORP [opp. angles to equal sides are equal] ………………..(1)

    Also in ΔOPR,

    ∠OPR+∠ORP+∠POR=180

    o

    (Angle sum property of triangle)

    ∠OPR+∠OPR+∠POR=180

    o

    from (1)

    2∠OPR+160=180

    o

    2∠OPR=180

    o

    −160

    o

    2∠OPR=20

    ∠OPR=20/2

    ∴∠OPR=10

    o

    .

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )