Question

State 'T' for true and 'F' for false. I. If one angle of a cyclic trapezium is four times the other, then the greater one measures 144∘. II. The length of the direct common tangent to two circles with radii R and r, having distance between the centres d, is √d2−(R−r)2

A

(I) F (II)F

B

(I) T (II)F

C

(I) T (II)T

D

(I) F (II)T

Solution

The correct option is C (I) T (II)T  I. T ∵ In cyclic quadrilateral (trapezium), Sum of opposite angles =180∘ ⇒x=4x=180∘⇒5x=180∘⇒x=36∘∴Greaterangle=4x=4×36∘=144∘ II. T,  The length of the direct common tangent to two circles with radii R and r, having distance between the centres d, is √d2−(R−r)2

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