In a triangle ABC the lengths of AB , BC and CA are 13,14 and 15 units respectively. The altitudes of the triangle ABC are concurrent at the point H and AD is the altitude on BC. The circum radius of the triangle ABC is

Question

In a triangle ABC the lengths of AB , BC and CA are 13,14 and 15 units respectively. The altitudes of the triangle ABC are concurrent at the point H and AD is the altitude on BC. The circum radius of the triangle ABC is (A)  (65/8) (B) (63/8) (C) (33/4) (D) (17/2)

Tardigrade Admin · Accepted Answer

Area of triangle ABC =(5 ⋅ 12+12 ⋅ 9/2)=30+54=84 ∴ R =( abc /4 Δ)=(13 ⋅ 14 ⋅ 15/4 ⋅ 84) R =(13 ⋅ 15/4 ⋅ 6)=(65/8) ⇒ (B)

Q. In a triangle $A BC$ the lengths of $A B, BC$ and $C A$ are 13,14 and 15 units respectively. The altitudes of the triangle $A BC$ are concurrent at the point $H$ and $A D$ is the altitude on $BC$ .
The circum radius of the triangle $A BC$ is

$\frac{65}{8}$

$\frac{63}{8}$

$\frac{33}{4}$

$\frac{17}{2}$

Area of triangle $A BC = \frac{5 \cdot 12 + 12 \cdot 9}{2} = 30 + 54 = 84$
$∴ R = \frac{ab c}{4Δ} = \frac{13 \cdot 14 \cdot 15}{4 \cdot 84}$
$R = \frac{13 \cdot 15}{4 \cdot 6} = \frac{65}{8} \Rightarrow (B)$

Q. In a triangle ABC the lengths of AB,BC and CA are 13,14 and 15 units respectively. The altitudes of the triangle ABC are concurrent at the point H and AD is the altitude on BC. The circum radius of the triangle ABC is

865​

863​

433​

217​