Question

Find the area of a right-angled triangle if radius of its circumcircle is 3 cm and altitude drawn to hypotenuse is 2 cm

Answer 1

hello friend,
-----Here is your answer-----


.circumcenter of the rt. angled triangle is at the mid point of the hypotenuse so the length of hypotenuse will be
6 cm
and length of altitude is 2cm
area of triangle is
$= ( \frac{1}{2} \times 6 \times 2 \: ) \: {cm}^{2}$
$= 6 \: {cm}^{2}$

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Answer 2

$\\ \boxed{ \rm \: let \: \triangle \: abc \: be \: right \: angled \: at \: B}$

$\textsf{Then hypotenus \: AC = diameter \: of \: its \: circumcircle}$

$\textsf{ = (2 × 3) = 6cm}$

$\textsf{Let BL⏊AC .Then,BL=2cm}$

$\textsf{Area of triangle ABC}= \rm \huge {\frac{1}{2}} \small ×AC×BL$

$\rm = \large \big( \frac{1}{2} \times 3 \times 2 \big)cm {}^{2} = 6cm {}^{2}$