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Tangents PA and PB are drawn to a circle with centre O and radius 6 cm such that ∠AOB = 120°. Find the area of quadrilateral OAPB.

Class 10Tangent Lengths and IncirclesGeometry

A $363 c m^{2}$
B $36 cm^{2}$
C $183 c m^{2}$
D $72 cm^{2}$

Step-by-Step Solution

∠APB = 60°, so ∠OPA = 30° and PA =

6 \div tan 30° = 63

cm. Area

= 2 \times \frac{1}{2} \times 6 \times 63 = 363

cm

^{2} .18 3

counts only one triangle.

Answer: A)

363 c m^{2}

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