Tangent to a Circle | Circles | Assessment | English | Grade 10

How many tangents can be drawn at a point on a circle?

• One

• Two

• Three

• Infinite

Answer explanation

At any point on a circle there can be one and only one tangent. So, option 1 is correct.

In the given figure, the radius of a circle with centre O is 4 cm. Line XY is a tangent at a point P. What is the measure of ∠ OPY? What is the distance of point O from the line XY?

• ∠OPY = 90⁰ Distance of point O from the line XY = 8 cm

• ∠OPY = 90⁰ Distance of point O from the line XY = 4 cm

• ∠OPY = 180⁰ Distance of point O from the line XY = 4 cm

• ∠OPY = 60⁰ Distance of point O from the line XY = 8cm

Answer explanation

In the given figure, OP is the radius = 4 cm We know that the distance between O and XY is OP since XY is touching the circle at only point P. So Distance of point O from the line XY = OP= Radius of circle = 4 cm we also know that,The tangent at any point of a circle is perpendicular to the radius through the point of contact. Hence, ∠ OPY = 90⁰ so the correct answer is Option 2.

A tangent XY at a point Y of a circle of diameter 24 cm meets a line through the centre O at point X so that OX = 37 cm. The length of the tangent XY is --

• 7 cm

• 17.5 cm

• 35 cm

• 70 cm

Answer explanation

With reference to the figure, Diameter of circle = 24 cm Radius of circle = OY = 12 cm Distance of X from O = OX = 37 cm In ∆ OYX, ∠ OYX = 90⁰ ( as tangent is perpendicular to radius at point of contact) So, By Pythagoras theorem, OX² = OY² + XY² XY²= 37² ─ 12² = 1369 ─ 144 = 1225 So, XY = √ 1225 = 35 cm So the correct answer is Option 3

Tags

CCSS.HSG.C.A.2

If the angle between two radii of a circle is 110⁰, then the angle between the tangents at the ends of the radii is ______

• 90⁰

• 50⁰

• 70⁰

• 40⁰

Answer explanation

With reference to the figure, OADB forms a quadrilateral We know that the sum of all four angles of a quadrilateral is 360⁰. So, ∠OAD + ∠ADB + ∠OBD + ∠BOA = 360⁰. ∠BOA = 110⁰ ( Given) ∠OAD = ∠OBD = 90⁰ ( as tangent is perpendicular to radius at point of contact) So, 90⁰ + ∠DBO + 90⁰ + 110⁰ = 360⁰ 290⁰ + ∠DBO = 360⁰ ∠DBO = 70⁰ So the correct answer is option 3.

Tags

CCSS.HSG.C.A.2

What is the distance between two parallel tangents of a circle if the area of the circle is 154cm² ?

• 7 cm

• 14 cm

• 21 cm

• 28 cm

Answer explanation

We know that the line segment joining the points of contact of two parallel tangents to a circle is a diameter of the circle. To calculate the diameter, first radius is needed to be calculated. Area of circle = π r² = 154 cm² r² = 154 / π = 154 x (7/ 22) = 49 i.e., r = 7 cm So, diameter = 2 x r = 2 x 7 = 14 cm. So, the distance between two parallel tangents = 14 cm Hence, the correct answer is option 2.

Tags

CCSS.7.G.B.4