40. Triangle PQR is a right triangle which is right angled at Q. QX perpendicular to PR,XY perpendicular to RQ and XZ perpendicular to PQ are drawn. Prove that ZX2=PZ x ZQ

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△ P Q R

Q, Q X ⊥ P R, X Y ⊥ R Q

X Z ⊥ P Q

X Z^{2} = P Z \times Z Q

△ P Q R, Q M

P R

P R^{2} - P Q^{2} = Q R^{2}

Q M^{2} = P M \times M R

In ∆PQR, PR > PQ, PA is the bisector of angle P and PM is perpendicular to QR. Prove that angle APM = 1/2 ( angle Q - angle R).

PQR is a right-angle triangle right angled at Q. XY is parallel to QR. PQ = 6 cm and PX : XQ = 1: 2. Calculate the lengths of PR and QR.

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