98 If tangent QR, PR, PQ are drawn respectively at A, B, C to the circle circumscribing an acute angled - Maths - Circles

Question

98 If tangent QR, PR, PQ are drawn respectively at A, B, C to the
circle circumscribing an acute angled AABC so as form another APQR,
then the RPQ is equal to A) 1800 - ZBAC C) 1800- 2 BAC D) ZBAC
%(180? - ZBAC) 99 In a frequency distribution, the mean and median
are 21 and 22 respectively, then the mode is approximately A) 25 5
24 0 C) 22 0 D) 20 5 100 In the given figure, If PQ Il RS,, then
the value of is XMY is

Rashi Lokwani · Accepted Answer

Dear Student,

Answer 98:
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5c657adb78c12%20png">

In quarilateral OBPC, ∠OBP = 90° and ∠OCP = 90° (A tangent is perpendicular to the radius at the point of contact)So, ∠OBP + ∠OCP = 90° + 90° = 180°  ⇒Opposite angles of quarilateral OBPC are supplementary
⇒quarilateral OBPC is a cyclic quadrilateralSo, ∠RPQ + ∠BOC =  180°  ∠RPQ = 180° - ∠BOCAlso, ∠BOC = 2∠BAC (Angle formed by a chord at the center is double the angle formed by the same chord at the circumference)⇒∠RPQ = 180° - 2∠BACAnswer : Option C

Answer 99:

Given, Mean = 21 and Median = 22

We know, Mean −Mode = 3 (Mean − Median)
21 - Mode = 3(21 - 22)
21 - Mode = 3 (-1)
21 - Mode = -3
Mode = 21 + 3
Mode = 24

Answer : Option B

Regards