Question

Suppose that p q and rs are two chords of a circle intersecting at a point o. It is given that p o = 3 cm and so = 4 cm. Moreover, the area of the triangle p or is 7 cm2 . Find the area of the triangle qos.

Answer 1

It is given that,

PQ ,RS are two chords of a circles intersecting at a point O.

PO = 3cm , SO = 4cm

Area of ∆POR = 7cm²

Proof:

Inscribed - angle theorem:

In ∆POR, ∆SQO,

<PRO = <SQO

/* Inscribed angles over PS*/

<RPO = <QSO

/* Inscribed angles over CD*/

<POR = <SOQ

∆POR ~ ∆SQO

/* The areas of two similar triangles are in the ratio of the squares of the two corresponding sides */

∆QOS/∆POR = (OS)²/(OP)²

=> ∆QOS/7 = 4²/3²

=> ∆QOS = (7×16)/9

=> area of ∆QOS = 112/9 cm²

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