In a triangle PQR, `anglePQR = 90^@` S is any point onQR. Prove that `PS^2+QR^2 = PR^2+QS^2`.

PQR is a triangle whose /_Q is right angle. If S is any point on QR, then prove that PS^(2) + QR^(2) =PR^(2) + QS^(2)

ABC is a right-angled isoscels triangles of which /_C is a right angle. If D is any point on AB. Then prove that AD^(2) + BD^(2) = 2CD^(2)

PQR is a triangle right angled at P and M is a point on QR such that PM bot QR . Show that PM^(2) = QM .MR.

In a triangle PQR, let anglePQR = 30^(@) and the sides PQ and QR have lengths 10 sqrt3 and 10, respectively. Then, which of the following statement(s) is (are) TRUE ? angleQPR = 45^(@) and The area of the triangle PQR is 25sqrt3 and angleQRP = 120^(@)

O is any point inside a rectangle. Prove that OA^2+OC^2=OB^2+OD^2 .

O is an internal point of the rectangle PQRS. Prove that OQ^(2)+OS^(2) = OP^(2) +QR^(2)

In Delta ACB, angle C = 90^(@) and CD bot AB Prove that (BC^(2))/(AC^(2)) = (BD)/(AD) .

In a right angled traingle PQR , angleP is right angle and PS is perpendicular to the hypetnuse QR. Prove that 1/(PS^2)-1/(PQ^2)=1/(PR^2)

Answer any Two questions : In triangle ABC angle C = 90^@ , If BC = m and AC = n then prove that m sin A+ n sin B = sqrt(m^2+ n^2)

In any triangle PQR, angleR = pi/2 . If tan 'P/2 and tan 'Q/2 are the roots of the equation ax^(2) + bx + c=0 (a ne 0) , then show that, a+b=c.