circle geometry
Asked by | 13th Mar, 2009, 03:12: PM
Given :2 circles with centrs O’ & O intersecting each other at A &B a tangent is drawn to circle with centre O’ at point A.
TPT: OA bisects angle CAB, i.e angle CAO = angle OAB
Construction : join OA,
Proof:
1. OA =
2. angle OAB =OBA….. BASE ANGLES
3. angle OAB +OBA+AOB =180o angle sum property
4. 2 OAB +AOB = 180o…….from (2)
5. also angle CAO +OAB+BAD =180o ……..CD is a straight line
6. equating ( 4) & (5) 2 OAB +AOB = CAO +OAB+BAD
7. OAB +AOB = CAO +BAD
8. but angle BAD = angle AOB………ANG IN ALTER SEGMENT
9. angle OAB = CAO from (7)
Hence proved
Answered by | 5th Jul, 2009, 03:31: PM
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