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Opposite & Adjacent Sides in a Right Angled Triangle

PQR is a tria...

Question

PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM² = QM × MR.

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Solution

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P M ⊥ Q R

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

P M ⊥ Q R

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

P Q R

P

M

Q R

P M ⊥ Q R

P M^{2} = Q M . M R

△ P Q R, P R^{2} - P Q^{2} = Q R^{2}

M

P R

Q M ⊥ P R

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

Δ P Q R,

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

Q M ⊥ P R

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

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PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM2 = QM × MR.