Tangents Circles and Right Triangles

What is the side across from the right angle called?

• Leg

• Pythagoras

• Hypotenuse

• Altitude

Angle between the tangent and radius at the point of contact is _ _ _ _ _

• 45

• 60

• 90

• 180

In the adjacent figure ACB

• 45

• 60

• 90

• 180

we can draw _ _ _ _ _ tangents to a given circle from a given point

• 1

• 2

• 3

• Infinite

The tangents drawn at the end of a diameter are _ _ _ _ _

• Parallel

• Zero

• Perpendicular

• None

In the figure given below ΔPQR is a right angled triangle with ∠P = 90°. The center of the incircle of the given triangle is O. Circles with centers O₁ and O₂ touch the circle and two sides as shown in the figure. If the radius of the incircle of ΔPQR is 1 cm and BR : BQ = 2:3, then find the value of r₁ : r₂ (where r₁ is the radius of circle with center O₁ and r₂ is the radius of circle with center O₂ ).

In the given figure PQ and PR are tangents of a semicircle. Center ‘O’ of this semicircle lies on QR. If QO = 2 cm and OR = 4 cm. If ∠P = 90^o the radius of the semicircle is:

PP¢ and QQ' are two direct common tangents to two circles intersecting at points A and B. The common chord on produced intersects PP' at R and 'QQ' at S. Which of the following is true?

• RA² + BS² = AB²

• RS² = PP' ² + AB²

• RS² = PP'² + QQ'²

• RS² = BS² + PP'²

• 26

• 25

• 24

• 23

Two circles C (O, r) and C (O', r') intersect at two points A and B and O lies on C (O', r'). A tangent CD is drawn to the circle C (O', r') at A. Then