Question

In the given diagram , TY is a tangent to the circle TVS . If <SVT = 48° and |VS| = |ST| . What is < VTY.​

Answer 1

∠VTY = 84°

Explanation:

because ΔTSV is isosceles (ST = SV) then ∠VTS = ∠SVT = 48°

Then ∠VST = 84° (180 - 48 - 48 = 84)

Well, I'm going back to the picture is worth a thousand words again.

Sketch attached:

A line from S to the center bisects ∠VST into two 42° angles.

A line from T to the center forms a 42° angle with line ST.

48°-42° = 6° = angle from perpendicular line CTR to line VT.

90° - 6° = 84° for ∠VTY

Answer 2

• 84°

Explanation:

∠VTY is the tangent chord angle

• Tangent chord angle is the half of the intercepted arc

∠TSV is the inscribed angle.

• Inscribed angle is the half of the intercepted arc

Since both of the mentioned angles refer to same arc, they are of same value.

• ∠VTY = ∠TSV

ΔTVS is isosceles as VS = ST, therefore the opposite angles are same.

• m∠T = m∠V = 48°

The measure of angle S

• m∠S = 180° - 2*48° = 84°

The required angle

• m∠VTY = 84°