If A(P-ABC) = 154 cm² and radius of the circle is 14 cm, find (1) ∠APC (2) l(arc ABC).

In figure 7.34, if A(P-ABC) = 154 cm² radius of the circle is 14 cm, find (1) ∠APC. (2) l(arc ABC).

Figure: circle with centre P; A and C are on the circle and B is on the minor arc AC.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

1 answer

Answer: (1) ∠APC = 90° (2) l(arc ABC) = 22 cm

(1) \(\dfrac{\theta}{360}\times\dfrac{22}{7}\times196=154\Rightarrow\dfrac{\theta}{360}\times616=154\)

\[\theta=\frac{154\times360}{616}=90^\circ\]

(2) Area \(=\dfrac{l\times r}{2}\Rightarrow154=\dfrac{l\times14}{2}\Rightarrow l=22\) cm.

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

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