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

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