A circle, center O passes through A, B, C and D. PDOB is a straight line. PAT is a tangent to the circle. Given that Triangle AOB = 112 degrees and AD=DC, Calculate by stating reasons,

a. Triangle APO
b. Triangle ACB
c. Triangle DCA

if the radius of the circle is 3 cm, calculate
d. length PA and PB.

a. You know that angle PAO is a right angle, and the sum of angles in a triangle is 180. You can find angle AOP since you know angle AOB and BOP is a straight line.

b. Remember that angles in the same segment are equal. You can find angle ADO easily either using the triangle AOD, or the property that the angle at the centre (AOB) is twice that at the circumference (ADB).

c. Find angle OAB using the triangle OAB and using the fact that OAB is an isosceles triangle with OA = OB. Deduce angle DCA using the fact again that angles in the same segment are equal.

d. You know the angle APO, hence using the sine ratio, evaluate AP.
Using the tangent ratio, evaluate OP and add the radius to get BP.

Quote:

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Originally Posted by Madihakazi

A circle, center O passes through A, B, C and D. PDOB is a straight line. PAT is a tangent to the circle. Given that Triangle AOB = 112 degrees and AD=DC, Calculate by stating reasons,

a. Triangle APO
b. Triangle ACB
c. Triangle DCA

if the radius of the circle is 3 cm, calculate
d. length PA and PB.

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Question doesn't make any sense.

• If point "P" is in line with "D", "O", and "B", it can't also be in line with the tangent at point "A" (unless it is the same point as "A").
• 112 degrees is one of the internal angles of triangle AOB?
• The length of the line AO is the same as the length of the line DC? Not unless C is the same point as D

.

I'm assuming that P is a point outside the circle. It's only point T that bugs me... I can't find any use in telling that there is a point T...

Thanks a lot sir... it is very helpful... Point P lies outside the circle and T is the other end of it and it does not have any sidnificance... your answer has guided me properly...

Thank you once again...