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 ${144}^{\circ }$.
II. The length of the direct common tangent to two circles with radii R and r, having distance between the centres d, is $\sqrt{d^2-(R-r{)}^2}$

• A. (I) F (II)F
• B. (I) T (II)F
• C. (I) T (II)T
• D. (I) F (II)T

Answer 1

The correct option is C

(I) T (II)T

I. T
$\because$ In cyclic quadrilateral (trapezium),
Sum of opposite angles =${180}^{\circ }$
$\Rightarrow x=4x={180}^{\circ }\Rightarrow 5x={180}^{\circ }\Rightarrow x={36}^{\circ }\therefore Greaterangle=4x=4\times {36}^{\circ }={144}^{\circ }$
II. T, The length of the direct common tangent to two circles with radii R and r, having distance between the centres d, is $\sqrt{d^2-(R-r{)}^2}$