Question

PQRS is a square.With centre P and radius =5cm an arc is drawn to cut SR at A and RQ at B.If AS=3cm then BR is equal to (a) 2cm (b) 1cm (c) 4cm (d) 3cm​

Answer 1

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Given :-

• PQRS is a square.
• With centre P and radius = 5cm
• An arc is drawn to cut SR at A and RQ at B.
• AS =3cm

To Find :-

• BR = ?

Solution :-

In right angle triangle PAS,

$\angle \: S = 90 \degree$

By Pythagoras Theorem,

$\to {PA }^{2} = {SA }^{2} + { PS}^{2} \\ \to {5}^{2} = {3}^{2} + { PS}^{2} \\ \to {PS}^{2} = 16 \\ \to \: PS = \sqrt{16} \\ \to \: PS = 4 \: cm$

In triangle PAS and triangle PBQ,

1. PS = PQ (as the sides of the square are equal)
2. PA = PB (as both are the radius of the same circle and are equal)
3. < S = < Q = 90° (angles of a square)

Hence, By SAS congruency,

PAS ≅ PBQ

Hence, It can be said as PS = QR = 4 cm and SA = QB = 3 cm.

Also,

BR = QR - QB

BR = 4 cm - 3 cm

BR = 1 cm

Final Answer :

• OPTION B - 1 cm

@SweetestBitter