Question

The orthocenter O of triangle ABC is interior of triangle ABC. If OB=AC and AD=10 cm, where AD is an Altitude, then AB equals


a) 20 root 2 cm

b) 10 root 2 cm

c) 20 cm

d) 5 root 2 cm​

Answer 1

Answer:

5√2

Step-by-step explanation:

........................

Answer 2

Answer:

In a triangle ABC, distance between vertices to ortho centre are 2RcosA, 2RcosB and 2RcosC from vertices A, B and C respectively

R is circumradius .

OB = 2RcosB

using sine formula

a/sinA = b/sinB = c/sinC = 2R

put 2R = b/ sinB

OB = bcosB/sinB

= b cotB =AC cotB

given

OB =AC

1= cotB

B = 45°

In triangle ABD;

sin45° = AD/AB

AB = AD/sin45° =10/1√2 = 10√2 cm

option (b) is correct.