Exercise 17C

### If I is the incentre of triangle ABC and AI when produced meets the circumcircle of triangle ABC in point D. If ∠BAC = 66o and ∠ABC = 80o. Calculate: (i) ∠DBC, (ii) ∠IBC,

Solution: Join $DB\text{ }and\text{ }DC,\text{ }IB\text{ }and\text{ }IC$ Given, if $\angle BAC\text{ }=\text{ }{{66}^{o~}}and~\angle ABC\text{ }=~{{80}^{o}}$ $I$ is the incentre of the...

Solution: Join $OE$ $Arc\text{ }EC$ subtends $\angle EOC$at the centre and $\angle EBC$at the remaining part of the circle. $\angle EOC\text{ }=\text{ }2\angle EBC\text{ }=\text{ }2\text{... read more ### Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base. Suppose, \[\vartriangle ABC,\text{ }AB\text{ }=\text{ }AC$and circle with $AB$ as diameter is drawn which intersects the side $BC\text{ }and\text{ }D$ And, join $AD$ Proof: It’s seen that,...

Solution: Firstly, join $OB\text{ }and\text{ }OC$ Proof: $\angle BOC\text{ }=\text{ }2\angle BAC\text{ }=\text{ }2\text{ }x\text{ }{{30}^{o}}~=\text{ }{{60}^{o}}$ Now, in $\vartriangle OBC$...
Solution: Now, $\angle ABD\text{ }=\angle ACD\text{ }=\text{ }{{30}^{o}}~$[Angles in the same segment] In $\vartriangle ADB$ by angle sum property we have \[\angle BAD\text{ }+\angle ADB\text{...