PRT is a tangent to a circle with centre O at the point R on it Diameter SQ of the circle is produce...........

Quantitative Aptitude (CGL) Geometry

PRT is a tangent to a circle with centre O, at the point R on it. Diameter SQ of the circle is produced to meet the tangent at P and

QRis joined. If $$\angle QRP = 28^\circ$$, then the measure of $$\angle$$SPR is:

This questions was previously asked in

SSC CGL 4th March 2020 Shift-2

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$$29^\circ$$

$$34^\circ$$

$$62^\circ$$

$$32^\circ$$

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Explanation:

$$\angle QRP = 28^\circ$$
$$\angle ORP = 90^\circ$$ (radius to tangent through pt of contact)
$$\angle QRO = \angle ORP - \angle QRP $$
$$\angle QRO = 90^\circ - 28^\circ = 62^\circ$$
Now,
$$\angle QRO = \angle OQR$$
($$ \because$$ OQ = OR(radius))
$$\angle OQR = 62^\circ$$
$$\angle RQP + \angle OQR = 180^\circ$$
$$\angle RQP = 180^\circ - 62^\circ = 118^\circ$$
In the $$\triangle$$OPR,
$$\angle SPR + \angle RQP + \angle QRP = 180^\circ$$
$$\angle SPR = 180^\circ - 118^\circ - 28^\circ = 34^\circ$$

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