Question

in triangle pqr, if pq=10cm and angleprq=90°,anglepqr=30°then find QR​

Answer 1

[math]S[/math] is the midpoint of the hypotenuse [math]PR.[/math]

With [math]S[/math] as centre, draw a circle with radius equal to [math]PS.[/math] Obviously, this circle will pass through points [math]P[/math] and [math]R.[/math]

[math]\angle PQR = 90^o.[/math]

[math]\Rightarrow \quad[/math] The circle will also pass through point [math]Q[/math] since [math]PR[/math] is a diameter of the circle and the measure of the angle subtended by the diameter on the circle is equal to [math]90^o.[/math]

$\Rightarrow \qquad SQ$

[math]\Rightarrow \qquad SQ[/math] is a radius of the circle.

[math]\Rightarrow \qquad QS = PS = 5[/math] cm.