In the given figure, PQRS is a square inscribed in a circle of radius 4 cm. PQ is produced till point Y. From Y a tangent is drawn to the circle at point R. What is the length (in cm) of SY?

A) $$4\sqrt {10} $$ B) $$2\sqrt {10} $$ C) $$6\sqrt {10} $$ D) $$3\sqrt 5 $$

Answer & Solution

Correct Answer: Option A

∠PRQ = 45°
∠ORY = 90°
∠QRY = 45°
RQ = QY
Diagonal = 8 = Diameter
Side $$ = \frac{8}{{\sqrt 2 }} = 4\sqrt 2 $$
In ΔSPY,
SY² = SP² + PY²
= 128 + 32
= 160
SY = $$4\sqrt {10} $$

Question posted by Examveda

Community

Join the Discussion

Join the discussion

Login to post a comment or share your explanation.

No comments yet Be the first to discuss this question.

Keep Learning

In the given figure PQRS is a square inscribed in a...

In the given figure, PQRS is a square inscribed in a circle of radius 4 cm. PQ is produced till point Y. From Y a tangent is drawn to the circle at point R. What is the length (in cm) of SY?

Join the Discussion

Related Questions on Geometry