Given:- PQ=QR, ANGLE P=60 DEGREE
TO FIND:- M(ARC PR)
SOLUTION:-????
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Answers
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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