In the given figure, PQR is a triangle in which PQ = PR and ∠PQR = 75°, then show that QR is equal to the radius of circumcircle of ∆PQR, whose centre is O.

In the given figure, PQR is a triangle in which PQ = PR and ∠PQR =

1.	In the given figure, PQR is a triangle in which PQ = PR and ∠PQR = 75°, then show that QR is equal to the radius of circumcircle of ∆PQR, whose centre is O.
Answer» PQR is a triangle in which PQ = PR and ∠PQR = 75°, To Find : show that QR is equal to the radius of CIRCUMCIRCLE of ∆PQR, whose centre is O. Solution :PQ = PR and ∠PQR = 75°, => ∠PRQ = 75° ∠PQR + ∠PRQ + ∠QPR = 180°=> 75° + 75° + ∠QPR = 180°=> ∠QPR = 30°∠QOR = 2 * ∠QPR ( angle by same CHORD at circle And center )=> ∠QOR = 2 * 30° = 60°in Δ QOR QO = OR = Radius=> ∠OQR = ∠ORQ ∠OQR = ∠ORQ + ∠QOR = 180°=> ∠OQR = ∠ORQ + 60° = 180°=> ∠OQR = ∠ORQ = 120°=> ∠OQR = ∠ORQ = 60°∠OQR = ∠ORQ = ∠QOR = 60°=> Δ QOR is EQUILATERAL Triangle=> QR = OQ = OR = Radius of circum circleQEDHence shown that QR is equal to the radius of circumcircle of ∆PQR, whose centre is O. Learn More:brainly.in/question/27315225show that (2,1) is the centre of the circumcircle of the triangle whose ...brainly.in/question/19339461find the coordinates of circumcentre and radius of circumcircle of ...brainly.in/question/3772960