Home
Class 12
MATHS
ABC is an acute angled triangle with cir...

ABC is an acute angled triangle with circumcenter O and orthocentre H. If AO=AH, then find the angle A.

Text Solution

Verified by Experts

Given that `OA = HA`
`rArr R = 2R cos A`
`rArr cos A = (1)/(2) " or " A = (pi)/(3)`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.1|12 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise Exercise 5.2|8 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise ARCHIVES (MATRIX MATCH TYPE )|1 Videos

  • PROPERTIES OF TRIANGLE, HEIGHT AND DISTANCE

    CENGAGE|Exercise Question Bank|15 Videos

Similar Questions

Explore conceptually related problems

In triangle ABC, line joining the circumcenter and orthocentre is parallel to side AC, then the value of t a n AtanCi se q u a lto sqrt(3) (b) 3 (c) 3sqrt(3) (d) none of these

Let ABC be an acute angled triangle whose orthocentre is at H. If altitude from A is produced to meet the circumcircle of triangle ABC at D , then prove H D=4RcosBcosC

Let ABC be an acute angled triangle with orthocenter H.D, E, and F are the feet of perpendicular from A,B, and C, respectively, on opposite sides. Also, let R be the circumradius of DeltaABC . Given AH.BH.CH = 3 and (AH)^(2) + (BH)^(2) + (CH)^(2) = 7 Then answer the following Value of R is

Let ABC be an acute angled triangle with orthocenter H.D, E, and F are the feet of perpendicular from A,B, and C, respectively, on opposite sides. Also, let R be the circumradius of DeltaABC . Given AH.CH = 3 and (AH)^(2) + (BH)^(2) + (CH)^(2) = 7 Then answer the following Value of HD.HF is

Let ABC be an acute angled triangle with orthocenter H.D, E, and F are the feet of perpendicular from A,B, and C, respectively, on opposite sides. Also, let R be the circumradius of DeltaABC . Given AH.CH = 3 and (AH)^(2) + (BH)^(2) + (CH)^(2) = 7 Then answer the following Value of (cos A. cos B : cos C)/(cos^(2)A + cos^(2)B + cos^(2)C) is

If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points (a^2+1,a^2+1) and (2a ,-2a), then find the orthocentre.

If H is the othrocenter of an acute angled triangle ABC whose circumcircle is x^2+y^2=16 , then circumdiameter of the triangle HBC is 1 (b) 2 (c) 4 (d) 8

If H is the othrocenter of an acute angled triangle ABC whose circumcircle is x^2+y^2=16 , then circumdiameter of the triangle HBC is (a)1 (b) 2 (c) 4 (d) 8

The distance between the circumcenter and the orthocentre of the triangle whose vertices are (0,0),(6,8), and (-4,3) is Ldot Then the value of 2/(sqrt(5))L is_________

Let A B C be a triangle having O and I as its circumcenter and incentre, respectively. If R and r are the circumradius and the inradius, respectively, then prove that (O I)^2=R^2-2R rdot Further show that the triangle B I O is a right angled triangle if and only if b is arithmetic mean of a and c.