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AB is the diameter of a semicircle k, C ...

`AB` is the diameter of a semicircle `k, C` is an arbitrary point on the semicircle (other than `A` or `B`) and `S` is the centre of the circle inscribed into triangle `ABC,` then measure of-

A

angle ASB changes as C moves on k

B

angle ASB is the same for all positions of C but it cannot be determined without knowing the radius

C

angle `ASB=135^(@)` for all positions of C

D

angle `ASB=150^(@)` for all positions of C

Text Solution

Verified by Experts

The correct Answer is:
C
`angleACB=90^(@)`, S is point of intersection of angle bisector hence `angleSAB+angleSBA=(90^(@))/(2)=45^(@)" "implies" "angleASB=135^(@)` for all C
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