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Topic Question Set

Q 1 :

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



(8)

Let O be the centre of the concentric circle of radii 5 cm and 3 cm respectively. Let AB be a chord of the larger circle touching the smaller circle at P

Then AP = PB and OP⊥AB

Applying Pythagoras theorem in ∆OPA, we have

OA2=OP2+AP2⇒25=9+AP2

⇒AP2=16⇒AP=4cm

      ∴ AB=2AP=8cm

Q 2 :

In the given figure, AB and CD are tangents to a circle centred at O. Is ∠BAC=∠DCA? Justify your answer.



Tangent to a circle from an external point are equal

RA = RC

So, ∠RAC=∠RCA

Let ∠RAC=∠RCA=x

We know that BAR and DCR are straight line.

∠BAC+∠CAR=180⁰

⇒∠BAC+x=180⁰

⇒∠BAC=180⁰–x

Similarly, ∠DCA=180⁰–x

So ∠BAC=∠DCA

Q 3 :

In the given figure, O is the centre of circle. Find ∠AQB, given that PA and PB are tangents to the circle and ∠APB = 75°.



∠PAO = ∠PBO = 90° ( angle between radius and tangent)

∠AOB = 105° (By angle sum property of a triangle)

∠AQB = ½ x 105° = 52.5° (Angle at the remaining part of the circle is half the angle subtended by the arc at the centre)