Question

in the given figure, P, Q and R are the mid-points of sides AB, AC and BC of triangle ABC respectively.
If AD perpendicular BC, then prove that PQRD is a cyclic quadrilateral.
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Answer 1

Step-by-step explanation:

content://[email protected]/images/screenshot/1605017143851339506189.png

Given:In △ABCP,Q and R are the midpoints of the sides

BC,CA and AB respectively.

Also,AD⊥BC

In a right-angled triangle, ADP,R is the midpoint of AB

∴RB=RD

⇒∠2=∠1 ........(1)

since angles opposite to the equal sides are equal.

Since,R and Q are the mid-points of AB and AC, then RQ∥BC

or RQ∥BP (by mid-point theorem)

Since,QP∥RB then quadrilateral BPQR is a parallelogram,

⇒∠1=∠3 ........(2)

since angles opposite to the equal sides are equal.

From equations (1) and (2),

∠2=∠3

But ∠2+∠4=180

∘

(by linear pair axiom)

∠3+∠4=180

∘

(∵∠2=∠3)

Hence ,quadrilateral PQRD is a cyclic quadrilateral.

Answer 2

Answer:

Step-by-step explanation: