Q1 of 26 Page 235

Choose the correct answer and give justification for each.

In the figure XY and X1Y1 are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X1Y1 at B then ∠AOB =



A. 80o


B. 100o


C. 90o


D. 60o


Construct Line OC = radius


OP = OQ = OC = radius


OC∥AP and AC∥OP and


Thus AP = OP = radius


As AP = OP and ∠P = 90°


ΔOAP is isosceles triangle


∴ ∠ PAO = ∠POA = 45°


Also ∠ PAC = 90°


∠OAC = 45° ---1


Also AB is perpendicular to OC


∠OCA = 90°


In ΔAOC


∠OCA + ∠OAC + ∠COA = 180°


45 + 90 + ∠COA = 180°


∠COA = 45°


Similarly


∠BOC = 45°


∴ ∠AOB = 90°

More from this chapter

All 26 →
1

Choose the correct answer and give justification for each.

If AP and AQ are the two tangents a circle with centre O so that ∠POQ = 110°, then ∠PAQ is equal to



A. 60o


B. 70o


C. 80o


D. 90o

 1

Choose the correct answer and give justification for each.

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80o, then ∠POA is equal to


A. 50o


B. 60o


C. 70o


D. 80o

 2

Two concentric circles of radii 5 cm and 3 cm are drawn. Find the length of the chord of the larger circle which touches the smaller circle.

 3

Prove that the parallelogram circumscribing a circle is a rhombus.