Question

21. In triangle ABC, midpoints of sides AB AC and BC are
P.Q and R respectively. AS LBC
Prove that OPQRS is a cyclic quadrilateral
SR
Fig. 2.102
195​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

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.

So,points P,Q,R and D are con-cyclic.

Hence the statement is true.

The answer is 0

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