Question

1. In the given figure, PQ=QR, angle P=60^ , Find m (arc PR).​

Answer 1

Answer:

Answer

⇒  In △PQR,

⇒  PR=QR                             [ Given ]

∴     ∠RPQ=∠PQR              [ Opp angles of equal sides are equal ]

⇒   ∠QRP=90o                     [ Angle inscribed in semi-circle ]

⇒  ∠PQR+∠QRP+∠RPQ=180o

⇒  ∠RPQ+90o+∠RPQ=180o

∴    2∠RPQ=180o−90o

∴    2∠RPQ=90o

∴    ∠RPQ=45o

Answer 2

Given:-

• PQ = QR .
• ∠P = 60° .

TO FIND :-

• Length of arc PR.

SOLUTION :-

in ∆PQR , we have,

→ ∠P = 60° (given)

→ PQ = QR (given)

then,

→ ∠P = ∠R . { Angle Opposite to equal sides are equal .}

So,

→ ∠P + ∠R + ∠Q = 180° (Angle sum Property.)

→ 60° + 60° + ∠Q = 180°

→ 120° + ∠Q = 180°

→ ∠Q = 180° - 120°

→ ∠Q = 60° .

Now, we know that,

• Angle at centre is double of angle at circumference .

so,

→ ∠POR = 2 * ∠Q = 2 * 60° = 120° . (where O is the centre of the circle.)

therefore,

→ Length of arc PR = (Angle at centre/360°) * 2 * π * radius

→ Length of arc PR = (120/360) * 2πr

→ Length of arc PR = (1/3)2πr = (1/3) of circumference of given circle. (Ans.)

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