The circumradius of a triangle is 9 cm while the inradius of it is 4 cm. What is the distance between the circumcentre and the incentre of the triangle?
Given:
The circumradius R = 9 cm
The inradius r = 4 cm
We need to find the distance between the circumcenter and the incenter of the triangle.
Formula Used:
The distance d between the circumcenter (O) and the incenter (I) of a triangle is given by the formula:
d
Where:
R is the circumradius
r is the inradius
Solution:
Substitute the given values into the formula:
d =
d =
d =
d =
The distance between the circumcenter and the incenter is 3 cm.
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90 Mins English English100 Questions100 Marks90 Mins English English40 Questions30 Marks25 Mins EnglishIn triangle ABC, medians AD, BE, and CF intersect at the centroid G. What is the ratio of the area of triangle GAB to the area of triangle ABC?
The circumradius of a triangle is 9 cm while the inradius of it is 4 cm. What is the distance between the circumcentre and the incentre of the triangle?
Read the given statements carefully and decide which option is correct with respect to the statements.
Statements:
1. In any triangle, the concurrent point of medians is a centroid.
2. In any triangle, the concurrent point of altitudes is an orthocentre.
3. In any triangle, the concurrent point of internal angular bisectors is an in-centre.
ABC is a right-angled triangle. If the lengths of two sides containing the right angle are 4 cm and 3 cm, the radius of its incircle is:
If the inradius of a triangle with perimeter 64 cm is 8 cm, then find the area of the triangle.
The mid points of AB and AC of a △ABC are X and Y, respectively. If BC+XY=18 units, then the value of BC-XY is:
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