Question

In the following figure, O is center of circle. Angle QPR=70° and m(arcPYR)= 160°, then find the value of each of the following:
1) m(arc QXR)
2) angle QOR
3) angle PQR​

Answer 1

Given- O is the centre of a circle in which an equilateral ΔPQR has been inscribed.

To find out- ∠QOR=?

Solution- The points P, Q & R are on the circumference of the circle since ΔPQR has been inscribed in the circle. Now the chord QR subtends ∠QOR to the centre O and ∠QPR to the circumference at P.

∴ By rule, ∠QOR=2∠QPR.........(i).

Now PQR is an equilateral Δ. Each of its angle is 60

o

. i.e ∠QPR=60

o

.

So, from (i), ∠QOR=2∠QPR=2×60

o

=120

o

.