In Fig. 14.97, BE ⊥ AC. AD is any line from A to BC intersecting BE in H, P, Q and R are respectively the mid points of AH, AB and BC. Prove that ∠ PQR = 90°

Question

In Fig. 14.97, BE &#x22A5; AC. AD is any line from A to BC intersecting BE in H, P, Q and R are respectively the mid points of AH, AB and BC. Prove that &#x2220; PQR = 90&#xB0;

Philoid · Accepted Answer

Given,

In ΔABC,

Q, R are the mid points of AB and AC

QR ⎸⎸AC.. (i)

In ΔABH,

Q, P are the mid points of AB and AH respectively,

QP ⎸⎸BH

QP ⎸⎸BE.. (ii)

But AC⌃BE therefore from (i) and (ii)

QP⌃QR

∠PQR = 90^∘

In Fig. 14.97, BE⊥AC. AD is any line from A to BC intersecting BE in H, P, Q and R are respectively the mid points of AH, AB and BC. Prove that ∠PQR = 90°