Q35 of 52 Page 10

In Fig. 3, AP and BP are tangents to a circle with center O, such that AP = 5 cm and ∠APB = 60 °. Find the length of chord AB. (CBSE 2016)

It is given in the question that,

∠ APB = 60o


We know that, tangents drawn from an external point of a circle are equal


∴ PA = PB


Also, we know that angles opposite to equal sides are equal


∴∠ PAB = ∠ PBA (i)


Sum of angles of a triangle = 180o


∴In triangle PAB, ∠ PAB + ∠ PBA + ∠ APB = 180o


∠ PAB + ∠ PAB + 60o = 180o


2 ∠ PAB = 120o


∠ PAB = 60o


∴


Hence, the sides AB and AP are equal to each other i.e. AB = AP = 5 cm

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