Question

In the figure AB = 12 cm, BC = 5 cm, AC = 13 cm

Angle B = 900

. Find the circumradius​

Answer 1

Answer:

$\huge\color {pink}\boxed{\colorbox{black} {✑Answer⁝}}$

From figure: △ABCis a right angled triangle

AC

2

=BC

2

+AB

2

AC

2

=(5)

2

+(12)

2

AC

2

=25+144

AC

2

=169=(13)

2

or AC=13

Now from figure,

i.cosA=

AC

AB

=

13

12

ii.cscA=

BC

AC

=

5

13

iii.cosC=

AC

BC

=

13

5

iv.cscC=

AB

AC

=

12

13

Hence, proved.

Answer 2

Answer:

Given:

In ΔABC,

AB = 5 cm, BC = 12 cm and AC = 13 cm

Formula Used:

Circumradius of a triangle(R) = abc/4Δ

Where, a, b and c are lengths of sides of triangle and Δ is area of triangle.

Calculation:

In ΔABC, AB = 5 cm, BC = 12 cm and AC = 13 cm

Now,

By Pythagoras theorem, we can see that

(13)2 = (12)2 + (5)2

So, ΔABC is a right angled triangle

Area of ΔABC = ½ × Base × Perpendicular

⇒ ½ × 5 × 12 = 30 cm2

⇒ Circumradius of a triangle(R) = abc/4Δ

⇒ R = (5 × 12 × 13)/(4 × 30)

⇒ 13/2 cm = 6.5 cm

∴ The circumradius of the ΔABC is 6.5