Q4 of 59 Page 83

In figure 3.84, O is the centre of the circle. Seg AB, seg AC are tangent segments. Radius of the circle isr and l(AB) = r , Prove that, is a square.


Given: AB = r = radius of the circle


Here, AB = AC = r {tangents from the same external point are equal}


And OB = OC = r = radius of the circle.


⇒ ∠ OBA = ∠ OCA = 90° Using tangent-radius theorem which states that a tangent at any point of a circle is perpendicular to the radius at the point of contact.


∵ sides of ABOC are equal and opposite angles are 90° each


Hence, ABOC is a square.


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2

Line l touches a circle with centre Oat point P. If radius of the circle is 9 cm,answer the following.

(1) What is d(O, P) = ? Why ?


(2) If d(O, Q) = 8 cm, where does thepoint Q lie?


(3) If d(PQ) = 15 cm, How manylocations of point R are line online l ? At what distance will eachof them be from point P?



 3

In figure 3.83, M is the centre of the circle and seg KL is a tangent segment.

If MK = 12, KL = then find -


(1) Radius of the circle.


(2) Measures of ∠ K and ∠ M.



 5

In figure 3.85, is a parallelogram. It circumscribes the circle with cnetre T. Point E,F, G, H are touching points. If AE = 4.5,EB = 5.5, find AD.


 6

In figure 3.86, circle with centre M touches the circle with centre N at point T. Radius RM touches the smaller circle at S. Radii of circles are 9 cm and 2.5 cm. Find the answers to the following questions hence find the ratio MS:SR.

(1) Find the length of segment MT


(2) Find the length of seg MN


(3) Find the measure of ∠ NSM.