Q5 of 59 Page 83

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.


Given: AE = 4.5, EB = 5.5


Here, AE = AH = 4.5 {tangents from same external point are equal}


EB = BF = 5.5{tangents from same external point are equal}


∵ Opposite sides of a parallelogram are equal


∴ AE = DG and EB = GC


Also, DH = DG = 4.5{tangents from same external point are equal}


And FC = GC = 5.5 {tangents from same external point are equal}


⇒ AD = AH + HD = 10


More from this chapter

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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.



 4

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.


 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.



 7

In the adjoining figure circles with centres X and Y touch each other at point Z. A secant passing through Z intersects the circles at points A and B respectively. Prove that, radius XA || radius YB. Fill in the blanks and complete the proof.


Construction: Draw segments XZ and ..YZ........ .


Proof: By theorem of touching circles, points X, Z, Y are ..concyclic........ .


..∠ YZB ........vertically opposite angles


Let ..... (I)


Now, seg XA ≅seg XZ ........ (...radius of the same circle.......)


= ....∠ XZA...... = a ........ (isosceles triangle theorem) (II)


similarly, seg YB ≅ .YZ......... ........ (.radius of the same circle.........)


.∠ZBY......... = a ........ (.isosceles triangle theorem.........) (III)


∴from (I), (II), (III),


∠ XAZ = .∠ ZBY.........


∴radius XA || radius YB .......... (..since alternate interior angles are equal........)