Question: Tangent Line

Comment on Tangent Line

You can also conclude that D=O/2= 50/2=25 as they both hold A and B, right?
gmat-admin's picture

Yes, since inscribed ∠ODB and central ∠AOB contain the same arc, we know that ∠ODB = (1/2)∠AOB
More here: https://www.gmatprepnow.com/module/gmat-geometry/video/880 (at 2:50)

Hi Brent, at 1:38 when you draw out the triangle BOD, could you please clarify as to why we can be confident in knowing that the other 2 angles must be 25 degrees each.

From my understanding, this rule applies ONLY to Right-angled Isosceles triangles (AKA the 1:1:√2 rule) However, trying BOD is not a right-angle triangle.

Appreciate you clarifying this rule.
gmat-admin's picture

Since O is the circle's center, we know that OB and OD are both radii.

Since all radii of a certain circle must be the same length, we know that OB = OD

If OB = OD, then ∆OBD is an isosceles triangle, which means ∠OBD = ∠ODB

Does that help?

Cheers,
Brent

Is it OK to assume that D is on the circle, if not mentioned? If that was a DS question, would we need to asume that D is or is not on the circle?

Cheers,

Philipp
gmat-admin's picture

If a point (or a vertex) appears to be on a line or curve, then we can assume that it does, indeed, lie on the line (or curve).
For more on what can and cannot be assumed, watch https://www.gmatprepnow.com/module/gmat-geometry/video/863

Cheers,
Brent

Hi brent,

Can we assume points A, O, D to be on a straight line ? I ask because the figure says drawn not to scale, so they may or may not be intending to be on a straight line ?
This could invalidate our assumption of the other angle being 130 degrees.

Thanks,
Karaan
gmat-admin's picture

Great question.
The "figure drawn not to scale" part only refers to the measurement of angles and lengths.
When it comes to lines, we can assume that, if it looks like a line, then it is a line.

The following video covers the assumptions we can and cannot make when it comes to geometric diagrams: https://www.gmatprepnow.com/module/gmat-geometry/video/863

Cheers,
Brent

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