Choose the correct alternative.
∠ACB is inscribed in arc ACB of a circle with centre O. If ∠ACB = 65°, find m(arc ACB).
Prove that, angles inscribed in the same arc are congruent.
Given: ∠PQR and ∠ PSR are inscribed in the same arc
Arc PXR is intercepted by the angles.
To prove: ∠ PQR ≅ ∠ PSR
m∠PQR = `1/2` m(arc PXR) ...(i) ______________
m∠________ = `1/2` m(arc PXR) ....(ii) ____________
∴ m∠ ________ = m∠PSR ....[From (i) and (ii)]
∴ ∠ PQR ≅ ∠ PSR ....(Angles equal in measure are congruent)
In the given figure, seg RS is a diameter of the circle with centre O. Point T lies in the exterior of the circle. Prove that ∠ RTS is an acute angle.