please answer these questions

### Asked by prasutally | 26th May, 2019, 08:20: AM

Expert Answer:

###
In the above figure,
O is the cerntre of a circle.
OA = 5 cm ..... radius of outer circle
AC = 8 cm .... chord of outer circle and tangent to the inner circle.
To find: OB = ? ..... radius of inner circle
OB is perpendicular to AC. .. (i) ( Tangent is perpendicular to radius at its point of contact)
We know that perpendicular from the centre of circle to the chord bisects the chord.
AB = 4 cm
In ΔOAB,

From (i)
By Pythagoras theorem, we get
OB^{2} = OA^{2} - AB^{2}
= 5^{2} - 4^{2}
= 25 - 16
= 9
→ OB = 3 cm

Therefore radius of the inner circle is 3cm.

^{2}= OA

^{2}- AB

^{2}

^{2}- 4

^{2}

### Answered by Yasmeen Khan | 27th May, 2019, 10:43: AM

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