Question

Construct $∆$LEM, such that, LE = 6 cm, LM = 7.5 cm, $\angle$LEM = 90$°$ and draw its circumcircle.

Answer 1

Steps of construction:
1. Draw a line segment LE=6 cm.
2. Draw $\angle \mathrm{LEB}=90°$.
3. With L as the centre and a radius of 7.5 cm, draw an arc cutting EB at M.
4. Join LM.
5. Then $∆$LEM is the required triangle.
6. Draw perpendicular bisectors of sides LE and LM (any two sides) which intersect at O.
7. Taking OL or OM or OE as the radius, draw the required circumcircle.