Question

(c) In the figure given below, O is centre of the circle and SP
is a tangent. If ZSRT -65°, find the values of x,y and z.
T
X
Q
P
2
у
659
R
S​

Answer 1

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Solution:

A cyclic quadrilateral is one in which sum of opposite angles are supplementary.

ie. Sum of opposite angles are = 180°

As Point P is an external point and from P two tangents of equal length PA and PB are drawn at circle.

From the Theorem of tangent,that radius drawn an angle of 90°

Thus

< OBP = 90°

< OAP = 90°

< OBP + < OAP = 90°+ 90°

< OBP + < OAP = 180°

these are the opposite angles of cyclic quadrilateral,and sum of both are 180°, thus sum of remaining two angles are also 180°

< AOB + < BPA = 180°

hence OAPB is a cyclic quadrilateral.

Hope it helps you.

Answer 2

Step-by-step explanation:

A cyclic quadrilateral is one in which sum of opposite angles are supplementary.

ie. Sum of opposite angles are = 180°

As Point P is an external point and from P two tangents of equal length PA and PB are drawn at circle.

From the Theorem of tangent,that radius drawn an angle of 90°

Thus

< OBP = 90°

< OAP = 90°

< OBP + < OAP = 90°+ 90°

< OBP + < OAP = 180°

these are the opposite angles of cyclic quadrilateral,and sum of both are 180°, thus sum of remaining two angles are also 180°

< AOB + < BPA = 180°

hence OAPB is a cyclic quadrilateral.

Hope it helps you.