Question

PQ =QR. Angle P = 60°, Find m (arc PR).​

Answer 1

Question:-

PQ = QR,Angle P = 60°, Find m (arc PR)

Required Answer :-

In ∆ PQR,

PQ = QR - (given)

Therefore, ∆ PQR is an isosceles triangle

- [ by isosceles triangle theorem ]

Angle P = Angle R = 60°

- [Angles of isosceles triangle]

Therefore Angle Q will be 60°

- [Remaining Angle of a triangle]

Now,

Angle Q = 1/2 x m(arc PR)

-[inscribed angle theorem]

60° = 1/2 x m(arc PR)

60 x 2 = m(arc PR)

120 = m(arc PR)

m(arc PR) = 120°

___________________________

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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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