9.4 Angles Subtended by an Arc

Step 1

Consider the major arc PR. The angle subtended at the circumference is $\angle PQR = 100^\circ$ .

Step 2

The angle subtended at the centre by the major arc is Reflex $\angle POR$ .

Step 3

Reflex $\angle POR = 2 \times \angle PQR = 200^\circ$ .

Step 4

The inner $\angle POR = 360^\circ - 200^\circ = 160^\circ$ .

Step 5

In $\Delta OPR$ , $OP = OR$ (Radii), so $\angle OPR = \angle ORP$ .

Step 6

Sum of angles: $160^\circ + 2\angle OPR = 180^\circ$ .

Step 7

$2\angle OPR = 20^\circ \implies \angle OPR = 10^\circ$ .

Final Answer

$10^\circ$

Operation

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Radius (r)

Chord Length (c)

Dist from Center (d)

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