Question

In the given figure , RST is the tangent to the circle with centre O, at S. AOS is a straight line BO || RT and ∠ORS = 46°. Then ∠BAC equals

(a) 22°

(b) 46°

(c) 23°

(d) 32°

Answer 1

Correct option is (c) 23°

Given, BO ∥ RT

∠BOC = ∠ORS = 46^∘        ...(Alternate angles)

Thus, ∠BAC = \(\frac 12\)​∠BOC 

= \(\frac 12\)​(46) 

= 23^∘

Angle subtended by the chord at the circle is half the angle subtended by the chord at the centre.