Could someone please help with these two questions?? (1 Viewer)

[extmathyo]

1. If AB, AC are two tangents to a circle and angle BAC = 84 degrees, what are the sizes of the angles in the two segments into which BC divides the circle?

2. P is a point within a circle of radius 13cm and XY is any chord drawn through P so that XP x PY = 25. Find the length of OP if O is the centre of the circle.

Please help, it would mean alot!!

 

[InteGrand]

1. If AB, AC are two tangents to a circle and angle BAC = 84 degrees, what are the sizes of the angles in the two segments into which BC divides the circle?

2. P is a point within a circle of radius 13cm and XY is any chord drawn through P so that XP x PY = 25. Find the length of OP if O is the centre of the circle.

Please help, it would mean alot!!

1. One of the angles is 84° (just BÂC, which is in one segment created by BC). The other angle is the angle in the other segment BC creates, which is 180° – 84° = 96°, since opposite angles of a cyclic quadrilateral are supplementary.

2. Draw the diameter through O and P, and label the length OP as x, so the distance from P to the end of the diameter on the same side of P as O is r – x, and the distance of O to the other endpoint of the diameter is r, where r = 13 cm is the radius.

Then using "products of intercepts of intersecting chords are equal", we get:

.

So .