Question : x, y, and z are the sides of a triangle. If z is the largest side and x² + y² > z², then the triangle is a:

Option 1: Isosceles right angled triangle

Option 2: Acute angled triangle

Option 3: Obtuse angled triangle

Option 4: Right angled triangle

Question : What is the position of the circumcenter of an obtuse-angled triangle?

Option 1: It lies inside the triangle.

Option 2: It lies outside the triangle.

Option 3: It is the mid-point of the largest side.

Option 4: It is the vertex opposite to the largest side.

Question : In a right-angled triangle PQR, right-angled at Q, the length of the side PR is 17 units, the length of the base QR is 8 units, and the length of the side PQ is 15 units. If $\angle RPQ = \sin\alpha $, then $\sin\alpha + \cos\alpha$ is:

Option 1: $\frac{18}{17}$

Option 2: $\frac{23}{17}$

Option 3: $\frac{21}{17}$

Option 4: $\frac{15}{17}$