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In the figure, Quadrilateral ABCD is …

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In the figure, Quadrilateral ABCD is circumscribing a circle with centre O and AD⊥ AB. If the radius of incircle is 10 cm, then the value of x is

Posted by C Akhilesh 4 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 4 years, 5 months ago

Let O be the mid point,

As = Ap ( tangent to the given circle)

and since L SAp is 90°

As = OP = Ap = 10cm ( radius)

Now, Let t be the point where Ap meets Cq

and we know that Cq = PR = 27 (tangent)

and Ct = 38 ( given in the fig)

» Cq + qt = 38

» 27cm + qt = 38cm

» qt = 38cm-27cm = 11cm

and now tp = tq ( tangent)

tp = 11cm

So to find x , i.e Apt

we have Apt = Ap + pt

= 10cm + 11cm = 21 cm

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