Question

In the adjoining figure,∆ABC is inscribed in a circle with center O. If <B=55°, find <BAC​

Answer 1

Step-by-step explanation:

Let AB be the chord of the given circle with centre O and a radius of 10 cm.

Then AB =16 cm and OB = 10 cm

From O, draw OM perpendicular to AB.

We know that the perpendicular from the centre of a circle to a chord bisects the chord.

∴ BM = (

16

2

) cm=8 cm

In the right ΔOMB, we have:

OB2 = OM2 + MB2 (Pythagoras theorem)

⇒ 102 = OM2 + 82

⇒ 100 = OM2 + 64

⇒ OM2 = (100 - 64) = 36

⇒ OM=

√

36

cm=6 cm

Hence, the distance of the chord from the centre is 6 cm.

Answer 2

in a circle every triangle is isocelous

therefore

if angle b is 55 angle c is also 55

so angle BAC= 180-(55+55)

=180-110

=70

answer is 70