Question

3
(A) Complete and write any one of the following activities :
(i) In the figure, a rectangle PQRS is inscribed in a
circle with centre T. Complete the following activity
to prove arc PQ = arc SR, arc SP = arc QR and
T
arc SPQ = arc PQR.
PQRS is a rectangle,
.. chord PQ = chord SR
(Opposite sides of a rectangle)
... arc PQ arc
(Arcs corresponding to congruent chords)
chord PS = chord QR
(Opposite sides of a rectangle)
... arc SP s arc
(Arcs corresponding to congruent chords)
.. measures of arcs SP and QR are equal.
Now, m(arc SP) + O + m (arc QR)
.. m(arc SPQ)
--
.. arc SPQ =​

Answer 1

Given :- In the figure, a rectangle PQRS is inscribed in a

circle with centre T.

To Prove :-

• arc PQ = arc SR,
• arc SP = arc QR
• arc SPQ = arc PQR.

Solution :-

given that, PQRS is a rectangle.

so,

→ chord PQ = chord SR (Opposite sides of a rectangle are equal.)

then,

→ arc PQ = arc SR (arcs corresponding to congruent chords.) (Proved) ----------- Eqn.(1)

similarly,

→ chord SP = chord QR (Opposite sides of a rectangle are equal.)

then,

→ arc SP = arc QR (arcs corresponding to congruent chords.) (Proved) ----------- Eqn.(2)

therefore,

→ m(arc SP) + m (arc PQ) = m (arc PQ) + m (arc QR)

→ m (arc SPQ) = m (arc PQR)

→ arc SPQ = arc PQR (Proved)

Learn more :-

In the figure, m (arc APC) = 100° and ∠BAC = 70°. Find i. ∠ABC ii. m (arc BQC).

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