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In Figure, a circle with centre O is ins...

In Figure, a circle with centre `O` is inscribed in a quadrilatal `A B C Ds u c ht h a t ,i ttou c h e ss i d e s` BC, AB, AD na `C D` AT POINTS P, Q, R and S respectively. If `A B=29c m ,A D=23 c m ,/_B=90^0` and `D S=5c m ,` then the radius of the circle (in cm) is 11 (b) 18 (c) 6 (d) 15

A

11

B

18

C

6

D

15

Text Solution

Verified by Experts

The correct Answer is:
option 1
`AB=29cm, AC=23cm, /_B=90^0 `and` DS=5cm `Given
`AQ=AR` ( tangents on the circle from external point A)
`DS=DR` ( tangents on the circle from external point D)
`CP=CS ` ( tangents on the circle from external point C)
`PB=BQ` ( tangents on the circle from external point B)
Also,` AB=AQ+BQ `
`DS=DR=5cm`
So, `AR = 23-5 =18cm`
...
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