(a) 9 : 4
(b) 3 : 4
(c) 9 : 8
(d) 8 : 3
Q4. If the circumcenter of a triangle lies on one of the sides then the orthocenter of the triangle lies on.
(a) One of the vertices
(b) On the same side of the triangle
(c) Outside of the triangle
(d) Strictly inside the triangle
Q5. The circumcenter and the orthocenter of a triangle coincides. Then
(a) The centroid also coincides with them
(b) The centroid will be different from them
(c) The triangle is isosceles
(d) The triangle is a right angle triangle
Q8. If RS is the diameter of the circle and ∠ PQS = 32° and PQ = PS. If then find the value of the ∠QSR =?
Q9. AB is a vertical pole and C is its middle point. The end A is on the level ground and P is any point on the level ground other than A the portion CB subtends an angle β at P. If AP : AB = 2 : 1 then β = ?
Q10. In a regular heptagon PQRSTUV, Lines PS and RU meet at point X. What is the value of ∠UXS?
Sol. If the circumcentre of the triangle lies on one of the sides of triangle then the given triangle is a right angle triangle hence the orthocenter will lie on one of its vertices.
Sol. If the circumcentre and the orthocenter of the triangle coincides then the given triangle is equilateral triangle hence option (a)