Question

In right angled triangle PQR, right angled at Q, X is the mid point of PR. prove that PX=XR=QX

Answer 1

Given :- In right angled triangle PQR, right angled at Q, X is the mid point of PR.

To Prove :-

• PX = XR = QX .

Concept used :-

• In right angled triangle , hypotenuse is the diameter of the circumcircle .

Answer :-

given that, in ∆PQR,

→ ∠PQR = 90°

so,

→ Side opposite to 90° = PR = Hypotenuse .

now, construct circumcircle of right angled ∆PQR .

then,

→ PR = Diameter of circle .

therefore,

→ PX = XR = QX = radius of circumcircle .

hence , we can conclude that,

→ PX = XR = QX (Proved).

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